Univ. Paris-Saclay

Service de Physique de l'Etat Condensé

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Riemann-invariant solutions of the isentropic fluid flow equations

Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
Grundland A.M. (Centre de recherches mathématiques, Université de Montréal, C.P. 6128, Montréal, Québec H3C 3J7, CANADA)
Huard B. (Département de mathématiques et de statistique, C.P. 6128, Succ. Centre-ville, Montréal, QC H3C 3J7, Canada)
Abstract:
We use a new version of the conditional symmetry method to obtain rank-k solutions expressed in terms of Riemann invariants of the isentropic compressible ideal fluid flow in 3+1 dimensions. We describe the procedure for constructing bounded solutions in terms of the elliptic Weierstrass p-function in detail.
Année de publication : 2009
Revue : Theor. Math. Phys. 159 752-762 (2009)
DOI : 10.1007/s11232-009-0063-x
Keywords : Riemann invariant - conditional symmetry method - rank-k solution - system of hydrodynamic type
Langue : Anglais

Elliptic general analytic solutions

Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
Musette M. (Vrije Universiteit Brussel, Belgium)
Abstract:
In order to find analytically the travelling waves of partially integrable autonomous nonlinear partial differential equations, many methods have been proposed over the ages: "projective Riccati method", "tanh-method", "exponential method", "Jacobi expansion method", "new ...", etc. The common default to all these "truncation methods" is to only provide some solutions, not all of them. By implementing three classical results of Briot, Bouquet and Poincare', we present an algorithm able to provide in closed form textit{all} those travellingz waves which are elliptic or degenerate elliptic, i.e. rational in one exponential or rational. Our examples here include the Kuramoto-Sivashinsky equation and the cubic and quintic complex Ginzburg-Landau equations.
Année de publication : 2009
Revue : Stud. Appl. Math. 123 63-81 (2009)
DOI : 10.1111/j.1467-9590.2009.00447.x
Preprint : arXiv:0903.2009v1
PACS : 02.30.Jr,02.30.Ik,42.65.Wi.
Keywords : elliptic solutions, Laurent series, Kuramoto-Sivashinsky equation, cubic and quintic complex Ginzburg-Landau equations.
Langue : Anglais

Fichier(s) à télécharger :
  • publi.pdf

  • Elliptic solutions of isentropic ideal compressible fluid flow in (3+1) dimensions

    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Grundland A.M. (Centre de recherches mathématiques, Université de Montréal, C.P. 6128, Montréal, Québec H3C 3J7, CANADA)
    Huard B. (Département de mathématiques et de statistique, C.P. 6128, Succ. Centre-ville, Montréal, QC H3C 3J7, Canada)
    Abstract:
    A modified version of the conditional symmetry method, together with the classical method, is used to obtain new classes of elliptic solutions of the isentropic ideal compressible fluid flow in (3 + 1) dimensions. We focus on those types of solutions which are expressed in terms of the Weierstrass weierp-functions of Riemann invariants. These solutions are of special interest since we show that they remain bounded even when these invariants admit the gradient catastrophe. We describe in detail a procedure for constructing such classes of solutions. Finally, we present several examples of an application of our approach which includes bumps, kinks and multi-wave solutions.
    Année de publication : 2009
    Revue : J. Phys. A 42 135203 (2009)
    DOI : 10.1088/1751-8113/42/13/135203
    Preprint : arXiv:0810.1905v2
    Lien : http://iopscience.iop.org/1751-8121/42/13/135203/pdf?ejredirect=.iopscience
    Langue : Anglais

    Explicit solutions of the four-wave mixing model

    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Bugaychuk S. (Institute of Physics, Kiev, Ukraine)
    Abstract:
    The dynamical degenerate four-wave mixing is studied analytically in detail. By removing the unessential freedom, we first characterize this system by a lower-dimensional closed subsystem of a deformed Maxwell-Bloch type, involving only three physical variables: the intensity pattern, the dynamical grating amplitude, the relative net gain. We then classify by the Painleve' test all the cases when singlevalued solutions may exist, according to the two essential parameters of the system: the real relaxation time tau, the complex response constant gamma. In addition to the stationary case, the only two integrable cases occur for a purely nonlocal response (Real(gamma)=0), these are the complex unpumped Maxwell-Bloch system and another one, which is explicitly integrated with elliptic functions. For a generic response (Re(gamma) not=0), we display strong similarities with the cubic complex Ginzburg-Landau equation.
    Année de publication : 2009
    Revue : J. Phys. A 42 FAST TRACK COMMUNICATION-192003 (2009)
    DOI : 10.1088/1751-8113/42/19/192003
    Preprint : arXiv:0903.5476v1
    Langue : Anglais

    Fichier(s) à télécharger :
  • publi.pdf

  • The Painlevé Handbook

    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Musette M. (~)
    Abstract:
    Nonlinear differential or difference equations are encountered not only in mathematics, but also in many areas of physics (evolution equations, propagation of a signal in an optical fiber), chemistry (reaction-diffusion systems), and biology (competition of species). This book introduces the reader to methods allowing one to build explicit solutions to these equations. A prerequisite task is to investigate whether the chances of success are high or low, and this can be achieved without any a priori knowledge of the solutions, with a powerful algorithm presented in detail called the Painlevé test. If the equation under study passes the Painlevé test, the equation is presumed integrable. If on the contrary the test fails, the system is nonintegrable or even chaotic, but it may still be possible to find solutions. The examples chosen to illustrate these methods are mostly taken from physics. These include on the integrable side the nonlinear Schrödinger equation (continuous and discrete), the Korteweg-de Vries equation, the Hénon-Heiles Hamiltonians, on the nonintegrable side the complex Ginzburg-Landau equation (encountered in optical fibers, turbulence, etc), the Kuramoto-Sivashinsky equation (phase turbulence), the Kolmogorov-Petrovski-Piskunov equation (KPP, a reaction-diffusion model), the Lorenz model of atmospheric circulation and the Bianchi IX cosmological model. Written at a graduate level, the book contains tutorial text as well as detailed examples and the state of the art on some current research.
    Année de publication : 2008
    Revue : Physique XXIV 256p.-6 illus. (2008)
    Lien : http://www.springer.com/physics/book/978-1-4020-8490-4
    Keywords : Painlevé equations, singularity analysis, exact solutions
    Langue : Anglais

    Doubly periodic waves of a discrete nonlinear Schrodinger system with saturable nonlinearity

    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Chow K.W. (Department of Mechanical Engineering, University of Hong Kong Pokfulam road, HONG KONG)
    Abstract:
    A system of two discrete nonlinear Schrodinger equations of the Ablowitz-Ladik type with a saturable nonlinearity is shown to admit a doubly periodic wave, whose long wave limit is also derived. As a by-product, several new solutions of the elliptic type are provided for NLS-type discrete and continuous systems.
    Année de publication : 2008
    Revue : J. Nonl. Math. Phys. 15 398-409 (2008)
    DOI : 10.2991/jnmp.2008.15.4.4
    Preprint : arXiv:0812.1196v1
    Langue : Anglais

    Fichier(s) à télécharger :
  • publi.pdf

  • Painlevé structure of a multi-ion electrodiffusion system

    Conte R. (Service de Physique de l’Etat Condensé, CEA Saclay, DSM/IRAMIS/SPEC, URA CNRS 2464, 91191 Gif-Sur-Yvette Cedex, France)
    Rogers C. (Department of Applied Mathematics, Hong Kong Polytechnic University, Kowloon, Hong Kong)
    Schief W. (Institut für Mathematik, Technische Universität Berlin, Straße des 17. Juni 136, D-10623 Berlin, Germany)
    Abstract:
    A nonlinear coupled system descriptive of multi-ion electrodiffusion is investigated and all parameters for which the system admits a single-valued general solution are isolated. This is achieved via a method initiated by Painlevé with the application of a test due to Kowalevski and Gambier. The solutions can be obtained explicitly in terms of Painlevé transcendents or elliptic functions.
    Année de publication : 2007
    Revue : J. Phys. A 40 F1031 (2007)
    DOI : 10.1088/1751-8113/40/48/F01
    Preprint : arXiv:0711.0615
    Langue : Anglais

    Fichier(s) à télécharger :
  • publi.pdf
  • 1751-8121_40_48_F01.pdf

  • Analytic structure of the four-wave mixing model in photorefractive materials

    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Bugaychuk S. (Institute of Physics, Kiev, Ukraine)
    Abstract:
    In order to later find explicit analytic solutions, we investigate the singularity structure of a fundamental model of nonlinear optics, the four-wave mixing model in one space variable z. This structure is quite similar, and this is not a surprise, to that of the cubic complex Ginzburg-Landau equation. The main result is that, in order to be single valued, time-dependent solutions should depend on the space-time coordinates through the reduced variable xi=sqrt{z} exp(-t / tau), in which tau is the relaxation time.
    Année de publication : 2008
    Preprint : arXiv:0806.1183v1
    Langue : Anglais

    Fichier(s) à télécharger :
  • publi.pdf

  • A closed-form solution in a dynamical system related to Bianchi IX

    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Abstract:
    The Bianchi IX cosmological model in vacuum can be represented by several six-dimensional dynamical systems. In one of them we present a new closed form solution expressed by a third Painleve function.
    Année de publication : 2008
    Revue : Phys. Lett. A 372 2269-2270 (2008)
    DOI : 10.1016/j.physleta.2007.11.042
    Preprint : arXiv:0712.0209v1
    Langue : Anglais

    Fichier(s) à télécharger :
  • publi.pdf

  • Partial integrability of the anharmonic oscillator

    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Abstract:
    We consider the anharmonic oscillator with an arbitrary-degree anharmonicity, a damping term and a forcing term, all coefficients being time-dependent: u" + g_1(x) u' + g_2(x) u + g_3(x) u^n + g_4(x) = 0, n real. Its physical applications range from the atomic Thomas-Fermi model to Emden gas dynamics equilibria, the Duffing oscillator and numerous dynamical systems. The present work is an overview which includes and generalizes all previously known results of partial integrability of this oscillator. We give the most general two conditions on the coefficients under which a first integral of a particular type exists. A natural interpretation is given for the two conditions. We compare these two conditions with those provided by the Painleve' analysis.
    Année de publication : 2007
    Revue : J. Nonlinear Math. Phys. 14-3 462-473 (2007)
    DOI : 10.2991/jnmp.2007.14.3.11
    PACS : 02.30.+g
    Keywords : Nonlinear differential equations, first integral, Painleve property, anharmonic oscillator, partial integrability
    Langue : Anglais

    Fichier(s) à télécharger :
  • paper.pdf
  • 10lig.pdf

  • On a capillarity model and the Davey-Stewartson I system: Quasi-doubly periodic wave patterns

    Rogers C. (School of Mathematics, University of New South Wales Sydney NSW 2052, AUSTRALIA)
    Chow K.W. (Department of Mechanical Engineering, University of Hong Kong Pokfulam road, HONG KONG)
    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Abstract:
    Année de publication : 2007
    Revue : Nuovo Cimento B 122 105-111 (2007)
    DOI : 10.1393/ncb/i2007-10050-3
    PACS : 47-35.-i,47.55.Ca,47.55.nb
    Keywords : Capillarity, Davey-Stewartson, wave patterns
    Langue : Anglais

    Fichier(s) à télécharger :
  • paper.pdf
  • 10lig.pdf
  • publi.pdf
  • RogersChowConte.accepted.08May2007.pdf

  • Painleve structure of a multi-ion electrodiffusion system

    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Rogers C. (School of Math., The Univ. of New South Wales, Sydney, AUSTRALIA)
    Schief W. (School of Math., The Univ. of New South Wales, Sydney, AUSTRALIA)
    Abstract:
    A nonlinear coupled system descriptive of multi-ion electrodiffusion is investigated and all parameters for which the system admits a single-valued general solution are isolated. This is achieved textit{via} a method initiated by Painleve' with the application of a test due to Kowalevski and Gambier. The solutions can be obtained explicitly in terms of Painleve' transcendents or elliptic functions.
    Année de publication : 2007
    Revue : J. Phys. A 40 F1031-F1040 (2007)
    Preprint : arXiv:0711.0615v1
    Langue : Anglais

    Fichier(s) à télécharger :
  • paper.pdf
  • 10lig.pdf
  • publi.pdf

  • Periodic waves of a discrete higher order nonlinear Schroedinger equation

    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Chow K.W. (Department of Mechanical Engineering, University of Hong Kong Pokfulam, Hong Kong, CHINA)
    Abstract:
    The Hirota equation is a higher order extension of the nonlinear Schroedinger equation by incorporating third order dispersion and one form of self steepening effect. New periodic waves for the discrete Hirota equation are given in terms of elliptic functions. The continuum limit converges to the analogous result for the continuous Hirota equation, while the long wave limit of these discrete periodic patterns reproduces the known result of the integrable Ablowitz-Ladik system.
    Année de publication : 2006
    Revue : Commun. Theor. Phys. 46 961-965 (2006)
    Preprint : arXiv:nlin.PS/0604010
    PACS : 02.30.Jr, 02.30.Ik, 42.65.Wi (PACS 2001) 30D30, 33E05, 35C05, 35Q55 (AMS MSC 2000)
    Keywords : Discrete higher order nonlinear Schrdinger equation; Discrete Hirota equation; Elliptic function solutions
    Langue : Anglais
    NB : 46, 961-965 (2006)

    Fichier(s) à télécharger :
  • 2006_CC_CTP_dhnls.pdf
  • paper.pdf
  • 10lig.pdf
  • publi.pdf

  • Analytic doubly periodic wave patterns for the integrable discrete nonlinear Schroedinger (Ablowitz-Ladik) model

    Chow K.W. (Department of Mechanical Engineering, University of Hong Kong Pokfulam, Hong Kong, CHINA)
    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Xu N. (Department of Mathematics, California Institute of Technology Pasadena, CA 91125, USA)
    Abstract:
    We derive two new solutions in terms of elliptic functions, one for the dark and one for the bright soliton regime, for the semi-discrete cubic nonlinear Schroedinger equation of Ablowitz and Ladik. When considered in the complex plane, these two solutions are identical. In the continuum limit, they reduce to known elliptic function solutions. In the long wave limit, the dark one reduces to the collision of two discrete dark solitons, and the bright one to a discrete breather.
    Année de publication : 2006
    Revue : Phys. Lett. A 349 422-429 (2006)
    DOI : 10.1016/j.physleta.2005.09.053
    Preprint : arXiv:nlin.PS/0509005
    PACS : 02.30.Jr, 02.30.Ik, 42.65.Wi
    Keywords : Discrete nonlinear Schrdinger equation, Ablowitz and Ladik model, elliptic function solutions.
    Langue : Anglais
    NB : 349, 422-429 (2006)

    Fichier(s) à télécharger :
  • ALwaves.03Sep2005.stripped.pdf
  • paper.pdf
  • ALwaves.06Apr2005.pdf
  • 10lig.pdf
  • publi.pdf

  • Symmetry reductions of a particular set of equations of associativity in twodimensional topological field theory

    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Gandarias M.L. (Departamento de Matematicas, Universidad de Cadiz Casa postale 40, E-11510 Puerto Real, Cadiz, SPAIN)
    Abstract:
    The WDVV equations of associativity arising in twodimensional topological field theory can be represented, in the simplest nontrivial case, by a single third order equation of the Monge-Ampere type. By investigating its Lie point symmetries, we reduce it to various nonlinear ordinary differential equations, and we obtain several new explicit solutions.
    Année de publication : 2005
    Revue : J. Phys. A 38 1187-1196 (2005)
    DOI : 10.1088/0305-4470/38/5/018
    Preprint : arXiv:math.AG/0412439
    Lien : http://stacks.iop.org/JPhysA/38/1187
    PACS : 02.20.Qs, 11.10.Lm (PACS 1995); 35Q58, 35Q99 (MSC 2000)
    Keywords : WDVV equations; Equations of associativity; Twodimensional topological field theory; Classical Lie symmetries; Reductions
    Langue : Anglais
    NB : 38, 1187-1196 (2005)

    Fichier(s) à télécharger :
  • 0412439.pdf
  • paper.pdf
  • 10lig.pdf
  • publi.pdf

  • Explicit integration of the Hénon-Heiles Hamiltonians

    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Musette M. (Tena)
    Verhoeven C. (Tena)
    Abstract:
    We consider the cubic and quartic Henon-Heiles Hamiltonians with additional inverse square terms, which pass the Painleve' test for only seven sets of coefficients. For all the not yet integrated cases we prove the singlevaluedness of the general solution. The seven Hamiltonians enjoy two properties: meromorphy of the general solution, which is hyperelliptic with genus two and completeness in the Painleve' sense (impossibility to add any term to the Hamiltonian without destroying the Painleve' property).
    Année de publication : 2005
    Revue : J. Nonl. Math. Phys. 12 212-227 (2005)
    Preprint : arXiv:nlin.SI/0412057
    Keywords : Henon-Heiles Hamiltonian; Separation of variables; Painleve property; Hyperelliptic
    Langue : Anglais
    NB : 12, 212-227 (2005) [Suppl. 1, Special Issue in Honor of Francesco Calogero on the Occasion of His 70th Birthday]
    Editeurs : Euler N.

    Fichier(s) à télécharger :
  • paper.pdf
  • 10lig.pdf
  • publi.pdf
  • 12s1_18.pdf

  • Another integrable case in the Lorenz model

    Yee T.-L. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Abstract:
    A scaling invariance in the Lorenz model allows one to consider the usually discarded case sigma=0. We integrate it with the third Painlev'e function.
    Année de publication : 2004
    Revue : J. Phys. A 37 L113-L115 (2004)
    DOI : 10.1088/0305-4470/37/10/L02
    Preprint : arXiv:nlin.CD/0402033
    Lien : http://stacks.iop.org/JPhysA/37/L113
    PACS : 02.30.-f, 05.45.+b, 47.27.-i
    Keywords : Lorenz model; First integral; Third Painlev equation
    Langue : Anglais
    NB : 37, L113-L115 (2004) [Lett. Ed.]

    Fichier(s) à télécharger :
  • paper.pdf
  • 10lig.pdf
  • publi.pdf
  • lorenz10r.pdf

  • A reduction of the resonant three-wave interaction to the generic sixth Painleve equation

    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Grundland M. (Centre de recherches mathématiques, Université de Montréal Montréal, Québec H3C 3J7, CANADA)
    Musette M. (Tena)
    Abstract:
    Among the reductions of the resonant three-wave interaction system to six-dimensional differential systems, one of them has been specifically mentioned as being linked to the generic sixth Painleve' equation P6. We derive this link explicitly, and we establish the connection to a three-degree of freedom Hamiltonian previously considered for P6.
    Année de publication : 2006
    Revue : J. Phys. A 39 12115-12127 (2006)
    DOI : 10.1088/0305-4470/39/39/S07
    Preprint : arXiv:nlin.SI/0604011
    Lien : http://stacks.iop.org/JPhysA/39/12115
    Keywords : Resonant three-wave interaction; Reduction; Sixth Painleve equation
    Langue : Anglais
    NB : 39, 12115-12127 (2006)

    Fichier(s) à télécharger :
  • paper.pdf
  • 10lig.pdf
  • publi.pdf
  • 0604011.pdf

  • Analytic solitary waves of nonintegrable equations

    Musette M. (Tena)
    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Abstract:
    Even if it is nonintegrable, a differential equation may nevertheless admit particular solutions which are globally analytic. On the example of the dynamical system of Kuramoto and Sivashinsky, which is generically chaotic and presents a high physical interest, we review various methods, all based on the structure of singularities, allowing us to characterize the analytic solution which depends on the largest possible number of constants of integration.
    Année de publication : 2003
    Revue : Physica D 181 70-79 (2003)
    Preprint : arXiv:nlin.PS/0302051
    PACS : 02.30.-f, 05.45.+b, 47.27.-i
    Keywords : Solitary waves; Cubic complex one-dimensional Ginzburg-Landau equation; Briot and Bouquet equations; Elliptic function; Genus; Truncation
    Langue : Anglais
    NB : 181, 70-79 (2003)

    Fichier(s) à télécharger :
  • paper.pdf
  • 10lig.pdf
  • publi.pdf
  • 0302051.pdf

  • Integration of a generalized Henon-Heiles Hamiltonian

    Verhoeven C. (Dienst Theoretische Natuurkunde, Vrije Universiteit Brussel, Pleinlaan 2, B-1050 Brussels)
    Musette M. (Dienst Theoretische Natuurkunde, Vrije Universiteit Brussel, Pleinlaan 2, B-1050 Brussels)
    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Abstract:
    The generalized H'enon-Heiles Hamiltonian $H=1/2(P_X^2+P_Y^2+c_1X^2+c_2Y^2)+aXY^2-bX^3/3$ with an additional nonpolynomial term $mu Y^{-2}$ is known to be Liouville integrable for three sets of values of $(b/a,c_1,c_2)$. It has been previously integrated by genus two theta functions only in one of these cases. Defining the separating variables of the Hamilton-Jacobi equations, we succeed here, in the two other cases, to integrate the equations of motion with hyperelliptic functions.
    Année de publication : 2002
    Revue : J. Math. Phys. 43 1906-1915 (2002)
    Preprint : arXiv:nlin.SI/0112030
    PACS : 45.20.Jj, 05.45.Yv
    Keywords : separation of variables, hyperelliptic functions, Henon-Heiles
    Langue : Anglais
    NB : 43, 1906-1915 (2002)

    Fichier(s) à télécharger :
  • paper.pdf
  • 10lig.pdf
  • publi.pdf

  • New contiguity relation of the sixth Painleve equation from a truncation

    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Musette M. (Dienst Theoretische Natuurkunde, Vrije Universiteit Brussel Pleinlaan 2, B-1050 Brussels, BELGIUM)
    Abstract:
    For the master Painleve equation P6(u), we define a consistent method, adapted from the Weiss truncation for partial differential equations, which allows us to obtain the first degree birational transformation of Okamoto. Two new features are implemented to achieve this result. The first one is the homography between the derivative of the solution $u$ and a Riccati pseudopotential. The second one is an improvement of a conjecture by Fokas and Ablowitz on the structure of this birational transformation. We then build the contiguity relation of P6, which yields one new second order nonautonomous discrete equation.
    Année de publication : 2002
    Revue : Physica D 161 129-141 (2002)
    Preprint : arXiv:nlin.SI/0112007
    PACS : 02.30.+g
    Keywords : Painleve equations, birational transformation, contiguity relation, Schlesinger transformation, singular, manifold method, truncation
    Langue : Anglais
    NB : 161, 129-141 (2002)

    Fichier(s) à télécharger :
  • publi.pdf

  • On the Schlesinger transformations of the sixth Painleve equation

    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Abstract:
    Following the recent discovery of two new Schlesinger transformations (ST) for the sixth Painlev'e equation, we give the interrelations between all the known STs. We thus isolate the unique one which at the same time conserves the independent variable and is not a product of other STs.
    Année de publication : 2001
    Revue : C.R. Acad. Sci. I Math. 332 501-504 (2001)
    Preprint : arXiv:math.CA/0103165
    PACS : 02.30.Gp, 02.30.Hq
    Numéro Exterieur : hal-00132588
    Langue : Français
    NB : 332, 501-504 (2001)

    Fichier(s) à télécharger :
  • stp6.pdf
  • paper.pdf
  • 10lig.pdf
  • publi.pdf

  • La physique mathematique : une discipline deja ancienne

    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Abstract:
    Année de publication : 2000
    Revue : Le Journal (CEA/Saclay) 6 (2000)
    Langue : Français
    NB : No 12, p. 7 (decembre 2000)
    Audience : Diffusion du savoir

    Fichier(s) à télécharger :
  • paper.pdf

  • Analytic expressions of hydrothermal waves

    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Musette M. (Dienst Theoretische Natuurkunde, Vrije Universiteit Brussel, Pleinlaan 2, B-1050 Bruxelles)
    Abstract:
    When subjected to a horizontal temperature difference, a fluid layer with a free surface becomes unstable and hydrothermal waves develop in the bulk. Such a system is modelized by two coupled amplitude equations of the one-dimensional, complex, cubic Ginzburg-Landau type. By transposing the method developed for one CGL3 equation, we obtain several new exact solutions expressed by closed form, singlevalued, analytic expressions. Some of them are the analogue of the famous amplitude hole solution of Bekki and Nozaki.
    Année de publication : 2000
    Revue : Rep. Math. Phys. 46 77-88 (2000)
    Preprint : arXiv:nlin.SI/0009022
    Keywords : coupled Ginzburg-Landau, exact solutions
    Langue : Anglais
    NB : 46, 77-88 (2000)

    Fichier(s) à télécharger :
  • paper.pdf
  • publi.pdf
  • torun.pdf

  • Comment on "Exact periodic solutions of the complex Ginzburg-Landau equation"

    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Musette M. (Dienst Theoretische Natuurkunde Vrije Universiteit Brussel B-1050 Brussel, BELGIQUE)
    Abstract:
    Année de publication : 1999
    Revue : J. Math. Phys. 40 5283 (1999)
    DOI : 10.1063/1.532675
    Lien : http://link.aip.org/link/?JMAPAQ/40/5283/1
    PACS : 02.90.+p, 03.40.Kf
    Keywords : Exact solutions, Ginzburg-Landau equation
    Langue : Anglais
    NB : 40, p. 5283 (1999)

    Fichier(s) à télécharger :
  • paper.pdf
  • 10lig.pdf

  • Integration by quadratures for an $N-$degree-of-freedom Hamiltonian system: Application to a Hénon-Heiles Hamiltonian

    Lewis H.R. (Dartmouth College, Department of Physics and Astronomy Hanover, New Hampshire 03755-3528, USA)
    Bouquet S. (DPTA/SPPE, CEA/Bruyères-le-Châtel BP 12, F-91680 Bruyères-le-Châtel, FRANCE)
    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Année de publication : 1998
    PACS : 03.20.+i, 46.10.+z, 46.90.+s
    Keywords : Hamilton's principal function; Integrability; Invariant; Hnon-Heiles system
    Langue : Anglais

    Fichier(s) à télécharger :
  • paper.pdf
  • 10lig.pdf

  • Backlund transformation of partial differential equations from the Painleve-Gambier classification, II. Tzitzeica equation

    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Musette M. (Dienst Theoretische Natuurkunde, Vrije Universiteit Brussel, B-1050 Brussel, BELGIQUE)
    Grundland A.M. (Centre de recherches mathématiques, Université de Montréal, C.P. 6128, Montréal, Québec H3C 3J7, CANADA)
    Abstract:
    From the existing methods of singularity analysis only, we derive the two equations which define the Bäcklund transformation of the Tzitzéica equation. This is achieved by defining a truncation in the spirit of the approach of Weiss et al., so as to preserve the Lorentz invariance of the Tzitzéica equation. If one assumes a third-order scattering problem, this truncation admits a unique solution, thus leading to a matrix Lax pair and a Darboux transformation. In order to obtain the Bäcklund transformation (BT), which is the main new result of this paper, one represents the Lax pair by an equivalent two-component Riccati pseudopotential. This yields two different BTs; the first one is a BT for the Hirota-Satsuma equation, while the second one is a BT for the Tzitzéica equation. One of the two equations defining the BT is the fifth ordinary differential equation of Gambier.
    Année de publication : 1999
    Revue : J. Math. Phys. 40 2092-2106 (1999)
    DOI : 10.1063/1.532853
    PACS : 02.90.+p, 03.40.Kf
    Keywords : Painleve analysis, Tzitzeica equation, Backlund transformation, Gambier classification
    Langue : Anglais

    Fichier(s) à télécharger :
  • paper.pdf
  • 10lig.pdf

  • Backlund transformation of partial differential equations from the Painleve-Gambier classification, I. Kaup-Kupershmidt equation

    Musette M. (Dienst Theoretische Natuurkunde, Vrije Universiteit Brussel, B-1050 Brussel, BELGIQUE)
    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Abstract:
    Among the 50 nonlinear second-order differential equations of Painlevé and Gambier, those which are linearizable provide a natural scheme for deriving the Lax pair and the Darboux transformation of a nonlinear partial differential equation when the order of the scattering problem is three. This new method allows one to obtain, from singularity analysis only, the Bäcklund transformation of the Kaup-Kupershmidt equation, a result which was missing until now.
    Année de publication : 1998
    Revue : J. Math. Phys. 39 5617-5630 (1998)
    DOI : 10.1063/1.532554
    PACS : 02.90.+p, 03.40.Kf
    Keywords : Painlev analysis, Gambier classification, Bcklund transformation, Kaup-Kupershmidt equation
    Langue : Anglais
    NB : 39, 5617-5630 (1998)

    On the exact solutions of the Bianchi IX cosmological model in the proper time

    Springael J. (Dienst Theoretische Natuurkunde, Vrije Universiteit Brussel, Pleinlaan 2, B-1050 Brussel, BELGIUM)
    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Musette M. (Dienst Theoretische Natuurkunde, Vrije Universiteit Brussel, Pleinlaan 2, B-1050 Brussel, BELGIUM)
    Abstract:
    It has recently been argued that there might exist a four-parameter analytic solution to the Bianchi IX cosmological model, which would extend the three-parameter solution of Belinskii et al. to one more arbitrary constant. We perform the perturbative Painleve test in the proper time variable, and confirm the possible existence of such an extension.
    Année de publication : 1998
    Revue : Regul. Chaotic Dyn. 3 3-8 (1998)
    Preprint : arXiv:solv-int/9804008
    Langue : Anglais
    NB : 3, 3-8 (1998)

    Fichier(s) à télécharger :
  • paper.pdf
  • 9804008.pdf
  • 10lig.pdf
  • publi.pdf

  • Discrete version of the Chazy class III equation

    Labrunie S. ()
    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Abstract:
    We study the discretization of the Chazy class III equation by two means: a discrete Painlevé test, and the preservation of a two-parameter solution to the continuous equation. In this way we achieve an optimal discretization scheme.
    Année de publication : 1996
    Revue : J. Phys. A 29 L499-L503 (1996)
    DOI : 10.1088/0305-4470/29/19/002
    Lien : http://stacks.iop.org/JPhysA/29/L499
    PACS : 02.30.Hq, 02.30.Ks, 02.30.Mv, 02.70.Bf
    Langue : Anglais
    NB : 29, L499-L503 (1996)

    Fichier(s) à télécharger :
  • s039_txt.pdf
  • paper.pdf
  • 10lig.pdf
  • publi.pdf

  • A new method to test discrete Painleve equations

    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Musette M. (Dienst Theoretische Natuurkunde, Vrije Universiteit Brussel, B-1050 Brussel, BELGIQUE)
    Abstract:
    Necessary discretization rules to preserve the Painlevé property are stated. A new method is added to the discrete Painlevé test, which perturbs the continuum limit and generates infinitely many no-log conditions.
    Année de publication : 1996
    Revue : Phys. Lett. A 223 439-448 (1996)
    DOI : 10.1016/S0375-9601(96)00783-9
    Langue : Anglais
    NB : 223, 439-448 (1996)

    Fichier(s) à télécharger :
  • paper.pdf
  • 10lig.pdf
  • publi.pdf
  • conte.pdf

  • A geometrical method towards first integrals for dynamical system

    Labrunie S. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Abstract:
    We develop a method, based on Darboux' and Liouville's works, to find first integrals and/or invariant manifolds for a physically relevant class of dynamical systems, without making any assumption on these elements' form. We apply it to three dynamical systems: Lotka--Volterra, Lorenz and Rikitake.
    Année de publication : 1996
    Revue : J. Math. Phys. 37 6198-6206 (1996)
    DOI : 10.1063/1.531772
    PACS : 02.30, 02.40, 02.90
    Langue : Anglais
    NB : 37, 6198-6206 (1996)

    Fichier(s) à télécharger :
  • paper.pdf
  • publi.pdf
  • s017_txt.pdf

  • The Painleve property, one century later

    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Abstract:
    The subject this volume is explicit integration, that is, the analytical as opposed to the numerical solution, of all kinds of nonlinear differential equations (ordinary differential, partial differential, finite difference). Such equations describe many physical phenomena, their analytic solutions (particular solutions, first integral, and so forth) are in many cases preferable to numerical computation, which may be long, costly and, worst, subject to numerical errors. In addition, the analytic approach can provide a global knowledge of the solution, while the numerical approach is always local. Explicit integration is based on the powerful methods based on an in-depth study of singularities, that were first used by Poincaré and subsequently developed by Painlevé in his famous Leçons de Stockholm of 1895. The recent interest in the subject and in the equations investigated by Painlevé dates back about thirty years ago, arising from three, apparently disjoint, fields: the Ising model of statistical physics and field theory, propagation of solitons, and dynamical systems. The chapters in this volume, based on courses given at Cargèse 1998, alternate mathematics and physics; they are intended to bring researchers entering the field to the level of present research.
    Année de publication : 1996
    Revue : Europhys. News 27 49 (1996)
    Langue : Anglais
    NB : 27, p. 49 (1996)

    Fichier(s) à télécharger :
  • paper.pdf
  • s013_txt.pdf
  • 10lig.pdf
  • publi.pdf

  • Non-Fuchsian extension to the Painleve test

    Musette M. (VUB Brussel, BELGIUM)
    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Abstract:
    We consider meromorphic particular solutions of nonlinear ordinary differential equations and perform a perturbation à la Poincaré making their linearized equation non-Fuchsian at the movable pole and Fuchsian at infinity. When the nonlinear equation possesses movable logarithms, they are detected sooner than with the perturbative (Fuchsian) Painlevé test.
    Année de publication : 1995
    Revue : Phys. Lett. A 206 340-346 (1995)
    DOI : 10.1016/0375-9601(95)00602-Y
    Numéro Exterieur : solv-int/9508003
    Langue : Anglais
    NB : 206, 340-346 (1995)

    Fichier(s) à télécharger :
  • paper.pdf
  • 10lig.pdf
  • publi.pdf
  • s112_txt.pdf

  • Exact solutions of the one-dimensional quintic complex Ginzburg-Landau equation

    Marcq P. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Chaté H. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Abstract:
    Exact solitary wave solutions of the one-dimensional quintic complex Ginzburg-Landau equations are obtained using a method derived from the Painlevé test for integrability. These solutions are expressed in terms of hyperbolic functions, and include the pulses and fronts found by van Saarloos and Hohenberg. We also find previously unknown sources and sinks. The emphasis is put on the systematic character of the method which breaks away from approaches involving somewhat ad hoc Ansätze.
    Année de publication : 1994
    Revue : Physica D 73 305-317 (1994)
    DOI : 10.1016/0167-2789(94)90102-3
    Langue : Anglais

    The two-singular manifold method: II. Classical Boussinesq system

    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Musette M. (Dienst Theoretische Natuurkunde Vrije Universiteit Brussel, B-1050 Brussel, BELGI\E)
    Pickering A. (Department of Mathematics, Heriot-Watt University Riccarton, Edinburgh, EH14 4AS, UNITED KINGDOM)
    Abstract:
    For pt.I see Musette et. al., ibid., vol.24, p.3895 (1994) The two-singular manifold method-a generalization of the singular manifold method of Weiss (1983)-is applied to the classical Boussinesq system, also known as the Broer-Kaup system. From the point of view of its singularity analysis, the important feature of this system is the existence of two principal families with opposite principal parts. The usual singular manifold method takes into account only one of these families at a time. Our generalization takes into account both families, and in this way we are able to derive the Lax pair and Darboux transformation-and hence the auto-Backlund transformation-for the classical Boussinesq system from its Painleve analysis.
    Année de publication : 1995
    Revue : J. Phys. A 28 179-187 (1995)
    DOI : 10.1088/0305-4470/28/1/020
    Lien : http://stacks.iop.org/JPhysA/28/179
    PACS : 0230, 0340K
    Numéro Exterieur : HWU94/12
    Langue : Anglais
    NB : 28, 179-187 (1995)

    Fichier(s) à télécharger :
  • paper.pdf
  • 10lig.pdf

  • The Bianchi Ix (MIXMASTER) Cosmological Model is Not Integrable

    Latifi A. (International Solvay Institutes of Physics and Chemistry Université libre de Bruxelles Campus Plaine CP 231, B-1050 Bruxelles, BELGIQUE)
    Musette M. (Dienst Theoretische Natuurkunde Vrije Universiteit Brussel Pleinlaan 2, B-1050 Brussel, BELGI\E)
    Conte R. (SACLAY)
    Abstract:
    The perturbation of an exact solution exhibits a movable transcendental essential singularity, thus proving the nonintegrability. Then, all possible exact particular solutions which may be written in closed form are isolated with the perturbative Painlev'e test; this proves the inexistence of any vacuum solution other than the three known ones.
    Année de publication : 1994
    Revue : Phys. Lett. A 194 83-92 (1994)
    Preprint : arXiv:gr-qc/9409025
    PACS : 02.30.+g, 04.20.Jb, 04.60.+n, 98.80.Dr
    Langue : Anglais
    NB : 194, 83-92 (1994); Erratum: Phys. Lett. A 197, 459-460 (1995)

    Fichier(s) à télécharger :
  • paper.pdf
  • 9409025.pdf
  • 10lig.pdf
  • publi.pdf

  • Auto-Backlund transformation and analytic solutions in one dimensional carrier flow equations

    Chen Z.J. (Department of Applied Mathematics, Shanghai Jiao Tong University Shanghai, CHINA)
    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Guo B. (Dept of Mathematics, Shanghai University of Science and Technology Shanghai, CHINA)
    Abstract:
    We consider the simplified one dimensional PDEâs governing the carrier flow in semi-conductor devices via the Painleve analysis approach, and obtain analytic solutions.
    Année de publication : 1993
    Revue : Acta Math. Sin., New Ser. 9 438-445 (1993)
    Langue : Anglais
    NB : 9, 438-445 (1993)

    Fichier(s) à télécharger :
  • paper.pdf
  • 10lig.pdf

  • The two-singular manifold method: I. Modified Korteweg-de Vries and sine-Gordon equations

    Musette M. (Dienst Theoretische Natuurkunde Vrije Universiteit Brussel B-1050 Brussel, BELGIUM)
    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Abstract:
    We address the problem of finding, by Painleve analysis only, the Backlund transformation of partial-differential equations (PDEs) having two families of movable singularities with opposite principal parts, such as the modified Korteweg-de Vries (MKdV), sine-Gordon or nonlinear Schrodinger equations. This first paper gives an almost algorithmic method which extends the singular-manifold method of Weiss(1986) that is unable to handle these equations. First, with only one singular manifold at a time, we obtain the Darboux transformation. Second, we assume that the ratio of two functions defining the singular manifolds satisfies the most general projective Riccati system with undetermined coefficients; the Darboux transformation then generates a very small number of determining equations, admitting a unique solution. Equivalent to the Lax pair of the Zakharov-Shabat-Ablowitz-Kaup-Newell-Segur scheme by the canonical linearization of the Riccati system. The method is here applied to the MKdV and sine-Gordon equations.
    Année de publication : 1994
    Revue : J. Phys. A 27 3895-3913 (1994)
    DOI : 10.1088/0305-4470/27/11/036
    Lien : http://stacks.iop.org/JPhysA/27/3895
    PACS : 0230, 0340 K
    Keywords : Korteweg-de Vries (KdV)
    Langue : Anglais
    NB : 27, 3895-3913 (1994)

    Fichier(s) à télécharger :
  • paper.pdf
  • 10lig.pdf

  • Factorization of the "classical Boussinesq" system

    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Musette M. (Dienst Theoretische Natuurkunde, Vrije Universiteit Brussel, Pleinlaan 2, B-1050 Brussel, BELGIUM)
    Pickering A. (Department of Mathematics, Herriot Watt University GB-Edinburgh EH14 4AS)
    Abstract:
    The scalar equation equivalent to the 'classical Boussinesq', or Broer-Kaup system, is shown to factorize into a differential operator acting on Burgers equation. The linearizability of this latter equation provides a very simple explanation for the recently found property of fusion and fission of a class of solitons for this system.
    Année de publication : 1994
    Revue : J. Phys. A 27 2831-2836 (1994)
    DOI : 10.1088/0305-4470/27/8/020
    Lien : http://stacks.iop.org/JPhysA/27/2831
    PACS : 0230, 0340K
    Langue : Anglais
    NB : 27, 2831-2836 (1994)

    Fichier(s) à télécharger :
  • boussi.pdf
  • paper.pdf
  • 10lig.pdf
  • publi.pdf

  • Linearity inside nonlinearity: exact solutions to the complex Ginzburg-Landau equation

    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Musette M. (Dienst Theoretische Natuurkunde Vrije Universiteit Brussel Pleinlaan 2, B-1050 Brussel, Belgium)
    Abstract:
    Systems of two linear partial differential equations (PDEs) with constant coefficients define a natural basis of elementary functions to build some exact solutions to nonlinear PDEs. For the one-dimensional complex Ginzburg- Landau equation, the usual representations of the complex field (Re A, or (A,Ā) are multivalued, which makes difficult the search for exact solutions in this manner. Fortunately, the Painlevé analysis naturally introduces an elementary single valued-like representation of A by two fields (Z,grad Θ), respectively complex abd real, uniquely defined by an explicit expression for Θ and A = ZeiΘ. Another important feature is the invariance by parity on A, which increases the class of expected solutions. This allows to retrieve quite easily the four famous solutions of Nozaki and Bekki, represented by the constant coefficients of two linear partial differential equations and a finite set of constants.
    Année de publication : 1993
    Revue : Physica D 69 1-17 (1993)
    DOI : 10.1016/0167-2789(93)90177-3
    PACS : 0230, 0340K, 4265
    Langue : Anglais
    NB : 69, 1-17 (1993)

    Fichier(s) à télécharger :
  • paper.pdf
  • 10lig.pdf

  • A perturbative Painleve approach to nonlinear differential equations

    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Fordy A.P. (University of Leeds, UK)
    Pickering A. (University of Leeds, UK)
    Abstract:
    We further improve the Painlevé test so that negative indices (âresonancesâ) can be treated: we demand single valuedness not only for any pole-like expansion as in the usual Painlevé test, but also for every solution close to it, represented as a perturbation series in a small parameter ε. Order zero is the usual test. Order one, already treated in a preliminary paper, reduces to a (linear) Fuchs analysis near a regular singularity and allows the introduction of all missing arbitrary coefficients. Higher orders lead to the analysis of a linear, Fuchsian type inhomogeneous equation. We obtain an infinite sequence of necessary conditions for the absence of movable logarithmic branch points, arising at every integer index, whether positive or negative, and at every order; those arising at negative indices, including -1, are new, while some conditions may not arise before some high perturbation order. We present several illustrative examples. We discuss the understanding of negative indices, and conclude that they are indistinguishable from positive indices, just as in the Fuchs theory. In particular, negative indices give rise to doubly infinite Laurent series.
    Année de publication : 1993
    Revue : Physica D 69 33-58 (1993)
    DOI : 10.1016/0167-2789(93)90179-5
    Langue : Anglais
    NB : 69, 33-58 (1993)

    Link between solitary waves and projective Riccati equations

    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Musette M. (Université de Bruxelles, Belgique)
    Abstract:
    Many solitary wave solutions of nonlinear partial differential equations can be written as a polynomial in two elementary functions which satisfy a projective (hence linearizable) Riccati system. From that property, the authors deduce a method for building these solutions by determining only a finite number of coefficients. This method is much shorter and obtains more solutions than the one which consists of summing a perturbation series built from exponential solutions of the linearized equation. They handle several examples. For the Henon-Heiles Hamiltonian system, they obtain several exact solutions; one of them defines a new solitary wave solution for a coupled system of Boussinesq and nonlinear Schrodinger equations. For a third order dispersive equation with two monomial nonlinearities, they isolate all cases where the general solution is single valued.
    Année de publication : 1992
    Revue : J. Phys. A 25 5609-5623 (1992)
    DOI : 10.1088/0305-4470/25/21/019
    Langue : Anglais
    NB : 25, 5609-5623 (1992)

    Link between solitary waves of NLPDE and Riccati equations

    Musette M. (Vrije Universiteit Brussel, Belgium)
    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Année de publication : 1991
    Langue : Anglais
    NB : Rapport interne SPEC-S91/086 (1991)

    Partial integrability of damped, forced, anharmonic oscillators

    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Abstract:
    Communication to : Proceedings of 'Nonlinear Coherent Structures in Physics and Biology', Dijon, 4-6 june, 1991
    Année de publication : 1991
    Lien : http://hdl.handle.net/10068/66477
    Keywords : Partial integrability of damped, forced, anharmonic oscillators [ differential equation; first integral; painleve property]
    Langue : Anglais
    NB : Rapport interne SPEC-S91/063 (1991)

    Algorithmic method for deriving Lax pairs from the invariant Painleve analysis of non-linear partial differential equations

    Musette M. (Dienst Theoretische Natuurkunde, Vrije Universiteit Brussel Pleinlaan 2, B-1050 Bruxelles, BELGIQUE)
    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Abstract:
    Given a partial differential equation, its Painlevé analysis will first be performed with a built-in invariance under the homographic group acting on the singular manifold function. Then, assuming an order for the underlying Lax pair, a multicomponent pseudopotential of projective Riccati type, the components of which are homographically invariant, is introduced. If the equation admits a classical Darboux transformation, a very small set of determining equations whose solution yields the Lax pair will be generated in the basis of the pseudopotential. This new method will be applied to find the yet unpublished Lax pair of the scalar HirotaâSatsuma equation. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.
    Année de publication : 1991
    Revue : J. Math. Phys. 32 1450-1457 (1991)
    DOI : 10.1063/1.529302
    Langue : Anglais
    NB : 32, 1450-1457 (1991)

    Invariant Painleve analysis of partial differential equations

    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Année de publication : 1989
    Revue : Phys. Lett. A 140 383-390 (1989)
    DOI : 10.1016/0375-9601(89)90072-8
    Langue : Anglais
    NB : 140, 383-390 (1989)

    Universal invariance properties of Painlevé analysis and Backlund transformation in nonlinear partial differential equations

    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Abstract:
    We define two transformations, independent of the polynomial PDE, making all the compatibility conditions at resonances and all the equations defining the Bäcklund transformation invariant by homographic transformation of the expansion function. The resulting dramatic shortening of invariant equations makes their solution feasible by hand, leading to new analytic solutions.
    Année de publication : 1988
    Revue : Phys. Lett. A 134 100-104 (1988)
    DOI : 10.1016/0375-9601(88)90942-5
    Langue : Anglais
    NB : 134, 100-104 (1988)

    Painleve analysis and Backlund transformation in the Kuramoto-Sivashinsky equation

    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Musette M. (Dienst Theoretische Natuurkunde, Vrije Universiteit Brussel Pleinlaan 2, B-1050 Bruxelles, BELGIQUE)
    Abstract:
    The authors apply the Painleve test to the Kuramoto-Sivashinsky nonlinear partial differential equation, which describes many interesting fluid motions. The equation passes the test in a weak sense. Although the Painleve analysis does not yield the general solution, they perform the Backlund transformation in order to obtain new particular solutions. The authors find explicitly all the solutions of the set of equations which define the Painleve-Backlund transformation: they reduce to only one type, namely the already known kink-shaped solitary wave.
    Année de publication : 1989
    Revue : J. Phys. A 22 169-177 (1989)
    DOI : 10.1088/0305-4470/22/2/006
    Langue : Anglais
    NB : 22, 169-177 (1989)

    Solution generale du pont de Wheatstone

    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    de Kouchkovsky R. (~)
    Abstract:
    Année de publication : 1987
    Langue : Français
    NB : Rapport interne SRM SPEC-S87/009 (1987)

    Erratum: On a labelling for point group harmonics. I and II [J. Math. Phys. 26, 2413, 2441 (1985)]

    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Raynal J. (SPHT, CEA/Saclay F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Abstract:
    Année de publication : 1986
    Revue : J. Math. Phys. 27 1169 (1986)
    DOI : 10.1063/1.527161
    Numéro Exterieur : SPhT-T85/100
    Langue : Anglais
    NB : 27, p. 1169 (1986)

    Swelling of an isolated polymer chain in a solvent

    des Cloizeaux J. (SPHT, CEA/Saclay F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Jannink G. (DRECAM/LLB, CEA/Saclay F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Abstract:
    In the framework of the continuous model, a precise expression of the swelling of an isolated polymer in solution is given for all values of the interaction. The perturbation series obtained by Muthukumar and Nickel (1984) constitutes the initial data and a « direct renormalization method » is used to get the final result (in three dimensions).
    Année de publication : 1985
    Revue : J. Physique Lett. 46 L595-L600 (1985)
    DOI : 10.1051/jphyslet:019850046013059500
    Numéro Exterieur : SPhT-T85/027
    Langue : Anglais
    NB : 46, L595-L600 (1985)

    Evidence for random strain at the cubic site of Yb$^3+$ in palladium by M\\össbauer spectroscopy on $^170$Yb

    Bonville P. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Abstract:
    Année de publication : 1985
    Revue : J. Physique 46 1553-1563 (1985)
    Langue : Anglais
    NB : 46, 1553-1563 (1985)

    Random walk with quaternion transfer probability on a bcc lattice

    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Fu H. (~)
    Hao B.-l. (~)
    Abstract:
    Année de publication : 1986
    Revue : Commun. Theor. Phys. 5 195-211 (1986)
    Langue : Anglais
    NB : 5, 195-211 (1986)

    On a labelling for point group harmonics. I. Cubic group

    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Raynal J. (SPHT, CEA/Saclay F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Abstract:
    Année de publication : 1985
    Revue : J. Math. Phys. 26 2413-2440 (1985)
    DOI : 10.1063/1.526757
    Langue : Anglais
    NB : 26, 2413-2440 (1985)

    Determination of point group harmonics for arbitrary J by a projection method. III. Cubic group, quantization along a ternary axis

    Raynal J. (SPHT, CEA/Saclay F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Année de publication : 1984
    Revue : J. Math. Phys. 25 3375-3381 (1984)
    Langue : Anglais
    NB : 25, 3375-3381 (1984)

    Determination of point group harmonics for arbitrary j by a projection method. I. Cubic group, quantization along an axis of order 4

    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Raynal J. (SPHT, CEA/Saclay F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Soulié E. (SPHT, CEA/Saclay F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Abstract:
    On donne une méthode de construction systématique des harmoniques cubiques. On construit des projecteurs sur des représentations
    Année de publication : 1984
    Revue : J. Math. Phys. 25 1176-1186 (1984)
    Numéro Exterieur : SPhT-T83/016
    Langue : Anglais
    NB : 25, 1176-1186 (1984)

    Extensions au systeme conversationnel TSO. Guide de l'utilisateur; guide du systeme

    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Abstract:
    Année de publication : 1981
    Langue : Français
    NB : Rapport interne SRM No 1949 (1981)

    More on spin orientation in MnO at 0K and zero applied field: theoretical predictions

    Bidaux R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Nasser J.A. (~)
    Abstract:
    Above its Néel temperature TN (~ 110 K), MnO has the f.c.c. crystalline structure, the point group of Mn++ ions being m3m. At TN an antiferromagnetic order takes place. Some properties of that order are well enough described by taking into account the exchange and dipolar interactions and the magneto-elastic coupling from exchange interactions. So : 1) exchange interactions are responsible for the two-sublattice antiferromagnetic structure, 2) dipolar interactions set the spins (for Mn++ L = 0 and S = 5/2) parallel to the (111) planes of the f.c.c. structure and 3) magneto-elastic coupling due to exchange creates a 3m symmetry strain tensor. In this article we study the effects of the magneto-elastic coupling coming from dipolar interactions. Although they are small, these effects are qualitatively important. So, the dipolar magneto-elastic coupling removes partially the spin orientation degeneracy. We show there are twelve antiferromagnetic domains in MnO, the spin direction of a domain being contained in the plane defined by the [111] and [100] axes of the f.c.c. structure and being nearly orthogonal to the [111] axis. Furthermore, this interaction creates in each domain a strain tensor of symmetry lower than 3m. All the results agree with those one can deduce from the experimental studies of MnO in a null magnetic field and null stress tensor. The above results are not qualitatively changed by application of a hydrostatic pressure or an uniaxial stress along the [111] axis. But we show that one could favour one among the twelve antiferromagnetic domains by applying a stress with components on both the [111] and [100] axes. Such a result would be very interesting for the magnetic study of MnO.
    Année de publication : 1980
    Revue : J. Physique 41 1317-1325 (1980)
    DOI : 10.1051/jphys:0198000410110131700
    Langue : Anglais
    NB : 41, 1317-1325 (1980)

    Order as an effect of disorder

    Villain J. (Département de Recherche Fondamentale, Laboratoire de diffraction neutronique, CEN, 85X, 38041 Grenoble Cedex, France)
    Bidaux R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Carton J.P. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Abstract:
    A generalized frustrated Ising model on a two-dimensional lattice is considered. This model is paramagnetic at zero temperature but ferromagnetic provided 0 < T < T c. The effect of dilution on this system is also investigated, and long range order is shown to be restored in the dilute model under certain conditions involving concentration, temperature and interactions which are discussed in comparison with usual percolation.
    Année de publication : 1980
    Revue : J. Physique 41 1263-1272 (1980)
    DOI : 10.1051/jphys:0198000410110126300
    Langue : Anglais
    NB : 41, 1263-1272 (1980)

    Exact solution of the planar motion of three arbitrary point vortices

    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    De Seze L. (~)
    Abstract:
    Année de publication : 1979
    Langue : Anglais
    NB : Rapport interne SRM No 1697 (1979)

    Comment on "Stable solutions for vortex systems"

    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Abstract:
    Année de publication : 1979
    Revue : Phys. Lett. A 75 87 (1979)
    Langue : Anglais
    NB : 75, p. 87 (1979)

    Frustration in periodic systems: exact results for some 2D Ising models

    André G. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Bidaux R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Carton J.P. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    De Seze L. (~)
    Abstract:
    We present exact results for various frustrated Ising models in two dimensions with periodic interactions. None of them gives rise to what could be regarded as spin glass order. The only long range orders encountered are of ferro- or antiferromagnetic type but the effect of frustration manifests itself at low temperature (entropy, susceptibilities). The analysis of these results provides some indications concerning a necessary condition for ordering in such systems and the possible nature of the spin glass order.
    Année de publication : 1979
    Revue : J. Physique 40 479-488 (1979)
    DOI : 10.1051/jphys:01979004005047900
    Langue : Anglais
    NB : 40, 479-488 (1979)

    Determination theorique de l'ordre d'un changement de phase displacif à d dimensions

    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Abstract:
    On étudie une transition displacive dans un cristal cubique à d dimensions, comportant par maille deux atomes dont l'un est assez lourd pour.être traité comme immobile. On suppose que les atomes légers ressentent un potentiel effectif anharmonique dû aux atomes lourds et sont couplés entre premiers voisins par un terme harmonique. Un traitement variationnel montre alors que la transition n'est du second ordre que pour une dimension supérieure à 4 et pour un couplage assez grand devant la partie harmonique du potentiel effectif ; dans tous les autres cas, en particulier à 3 dimensions, le modèle donne une transition du premier ordre.
    Année de publication : 1974
    Revue : J. Physique 35 67-70 (1974)
    DOI : 10.1051/jphys:0197400350106700
    Keywords : ferroelectric transitions – solid state phase transformations
    Langue : Français
    NB : 35, 67-70 (1974)

    VFORM - Utilisation conversationnelle du langage Formac

    Conte R. (~)
    Renardy J.F. (~)
    Année de publication : 1971
    Langue : Français
    NB : Rapport interne SRM No 921 (1971)

    Influence de l'ordre à grande distance sur les constantes elastiques d'alliages ordonnes : application au laiton beta

    Conte R. (~)
    Pick R.M. (~)
    Abstract:
    On présente ici une étude cohérente de l'influence de l'ordre à grande distance sur le paramètre cristallin et le spectre de phonons du laiton Beta, en utilisant l'approximation du champ moléculaire. L'introduction de pseudo-potentiels proportionnels à la charge des ions permet alors d'expliquer la variation des coefficients élastiques de cet alliage en fonction de la température. L'accord entre la théorie et les résultats expérimentaux est satisfaisant eu égard aux approximations utilisées.
    Année de publication : 1969
    Revue : J. Physique 30 451-460 (1969)
    DOI : 10.1051/jphys:01969003005-6045100
    Keywords : copper alloys – crystal atomic structure of alloys – elastic constants – lattice dynamics
    Langue : Français
    NB : 30, 451-460 (1969)


    50 dans la catégorie Proceedings

    A reduction of the resonant three-wave interaction to the generic sixth Painlevé equation

    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Grundland A.M. (Centre de recherches mathématiques, Université de Montréal)
    Musette M. (Tena)
    Abstract:
    Among the reductions of the resonant three-wave interaction system to six-dimensional differential systems, one of them has been specifically mentioned as being linked to the generic sixth Painlevé equation P6. We derive this link explicitly, and we establish the connection to a three-degree-of-freedom Hamiltonian previously considered for P6.
    Année de publication : 2006
    Revue : J. Phys. A 39 12115 (2006)
    chapitre de livre : in: Proceedings of Asymptotic methods in nonlinear wave phenomena (Workshop in honor of the 65th birthday of Antonio Greco)
    Maison d'édition : World Scientific, Singapore, 2007
    conférence invité : in: Proceedings of Asymptotic methods in nonlinear wave phenomena : Proceedings of Asymptotic methods in nonlinear wave phenomena in: Proceedings of Asymptotic methods in nonlinear wave phenomena (Workshop in honor of the 65th birthday of Antonio ; Palermo, Italy ; 2006-06-05 / 2006-06-07
    DOI : 10.1088/0305-4470/39/39/S07
    PACS : 02.30.Hq, 02.30.Ik
    Keywords : Resonant three-wave interaction; Reduction; Sixth Painlev equation
    Langue : Anglais
    Editeurs : Ruggeri T., Sammartino M.

    Fichier(s) à télécharger :
  • paper.pdf
  • 10lig.pdf

  • Integration of partially integrable equations

    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Année de publication : 2006
    chapitre de livre : in: Proceedings of the 13th Conference on Waves and stability in continuous media (WASCOM 2005)
    Maison d'édition : World scientific, Singapore, 2006
    conférence invité : in: Proceedings of the 13th Conference on : Proceedings of the 13th Conference on in: Proceedings of the 13th Conference on Waves and stability in continuous media (WASCOM 2005) ; Acireale, Catania, Italy ; 2005-06-19 / 2005-06-25
    Preprint : arXiv:nlin.SI/0604063
    PACS : 02.30.H,42.65
    Keywords : Kuramoto-Sivashinsky equation, Nevanlinna theory, Painlev test, elliptic functions
    Langue : Anglais
    Editeurs : Monaco R., Mulone G., Rionero S., Ruggeri T.

    Fichier(s) à télécharger :
  • paper.pdf
  • Acirealenlin.pdf
  • 10lig.pdf
  • publi.pdf

  • On the Lax pairs of the sixth Painleve equation

    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Abstract:
    The dependence of the sixth equation of Painleve' on its four parameters (2 alpha,-2 beta,2 gamma,1-2 delta) =(theta_{infty}^2,theta_{0}^2,theta_{1}^2,theta_{x}^2) is holomorphic, therefore one expects all its Lax pairs to display such a dependence. This is indeed the case of the second order scalar "Lax" pair of Fuchs, but the second order matrix Lax pair of Jimbo and Miwa presents a meromorphic dependence on theta_infty (and a holomorphic dependence on the three other theta_j). We analyze the reason for this feature and make suggestions to suppress it.
    Année de publication : 2007
    Revue : RIMS Kokyuroku B2 21-27 (2007)
    conférence invité : Japanese-French Symposium on Algebraic, analytic and geometric aspects of complex differential equations and their deformations. Painlev hierarchies ; Kyoto University, Kyoto, Japan ; 2006-05-15 / 2006-05-20
    Preprint : arXiv:nlin.SI/0701049
    PACS : 02.20.Qs,11.10.Lm
    Keywords : Sixth Painlev function, Fuchsian system, Lax pair, apparent singularity, isomonodromic deformation
    Langue : Anglais
    NB : B2, 21-27 (2007)
    Editeurs : Takei Y.

    Fichier(s) à télécharger :
  • paper.pdf
  • 10lig.pdf
  • publi.pdf
  • conte.pdf
  • 0701049.pdf

  • Analytic patterns for chaotic equations

    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Revue : Int. J. Mod. Phys. B (submitted)
    conférence invité : International Conference on the Frontiers of Nonlinear and Complex Systems ; Hong-Kong, China ; 2006-05-24 / 2006-05-26
    PACS : 02.30.+g
    Keywords : Chaotic equation, closed form solution, elliptic
    Langue : Anglais
    Editeurs : Li B., Tang L.-H.

    Fichier(s) à télécharger :
  • paper.pdf
  • 10lig.pdf

  • Integration of partially integrable evolution equations

    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Année de publication : 2006
    chapitre de livre : in: Proceedings of the XIII International Conference on Waves and Stability in Continuous Media (WASCOM05)
    Maison d'édition : World Scientific, Singapore, 2006
    Pages : pp. 146-157
    conférence invité : in: Proceedings of the XIII International : Proceedings of the XIII International in: Proceedings of the XIII International Conference on Waves and Stability in Continuous Media (WASCOM05) ; Acireale, Catania, Italy ; 2005-06-19 / 2005-06-25
    Preprint : arXiv:nlin.SI/0604063
    PACS : 02.30.H, 42.65
    Keywords : Kuramoto-Sivashinsky equation; Nevanlinna theory; Painlev test; Elliptic functions
    Langue : Anglais
    Editeurs : Monaco R., Mulone G., Rionero S., Ruggeri T.

    Fichier(s) à télécharger :
  • paper.pdf
  • Acirealenlin.pdf
  • 10lig.pdf
  • publi.pdf

  • Hamiltonians with two degrees of freedom admitting a singlevalued general solution

    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Musette M. (Tena)
    Verhoeven C. (Tena)
    Année de publication : 2005
    Revue : Anal. Theory Appl. 21 188-200 (2005)
    conférence invité : in: Proceedings of the International Conference on Analysis and Its Applications (ICAA 2004) ; Nanjing, China ; 2004-07-20 / 2004-07-24
    Preprint : arXiv:nlin.SI/0507012
    PACS : 02.30.Hq, 03.40
    Keywords : Hnon-Heiles Hamiltonian; Painlev property; Hyperelliptic
    Langue : Anglais
    NB : 21, 188-200 (2005)
    Editeurs : Chen J.-C., Conte R., Fitzgerald C., Hsu L.-C., Su W.-Y., Yang C.-C., Zhu K.-H.

    Fichier(s) à télécharger :
  • 0507012.pdf
  • paper.pdf
  • 10lig.pdf
  • publi.pdf

  • Painleve property of the Henon-Heiles Hamiltonians

    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Musette M. (Tena)
    Verhoeven C. (Tena)
    Abstract:
    Time independent Hamiltonians of the physical type H = (P_1^2+P_2^2)/2+V(Q_1,Q_2) pass the Painleve' test for only seven potentials V, known as the He'non-Heiles Hamiltonians, each depending on a finite number of free constants. Proving the Painleve property was not yet achieved for generic values of the free constants. We integrate each missing case by building a birational transformation to some fourth order first degree ordinary differential equation in the classification (Cosgrove, 2000) of such polynomial equations which possess the Painleve property. The properties common to each Hamiltonian are: (i) the general solution is meromorphic and expressed with hyperelliptic functions of genus two, (ii) the Hamiltonian is complete (the addition of any time independent term would ruin the Painleve property).
    Année de publication : 2006
    chapitre de livre : International Conference on Asymptotic Theories and Painleve Equations / Theories asymptotiques et equations de Painleve
    conférence : International Conference on Asymptotic Theories and Painleve International Conference on Asymptotic Theories and Painlev Equations / Thories asymptotiques et quations de Painlev ; Universite d'Angers, France ; 2004-06-01 / 2004-06-05
    Preprint : arXiv:nlin.SI/0604012
    PACS : Primary 34M60; Secondary 34E20, 34M55, 34M35 (2000 MSC)
    Keywords : Henon-Heiles Hamiltonian; Painleve property; Hyperelliptic; Separation of variables; Darboux coordinates
    Langue : Anglais
    NB : 14, 21-38 (2006) (Societe Mathematique de France)
    Editeurs : Delabaere E., Loday-Richaud M.

    Fichier(s) à télécharger :
  • paper.pdf
  • Angers.pdf
  • 10lig.pdf
  • publi.pdf

  • On the Lax pairs of the continuous and discrete sixth Painleve equations

    Lin R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Musette M. (Tena)
    Abstract:
    Among the recently found discretizations of the sixth Painleve equation P6, only the one of Jimbo and Sakai admits a discrete Lax pair, which does establish its integrability. However, a subtle restriction in this Lax pair prevents the possibility to generalize it in order to find the other missing Lax pairs. It happens that the same restriction already exists in the matrix Lax pair of Jimbo and Miwa for the continuous P6. In this preliminary article, we remove this last restriction and give a matrix Lax pair for P6 which is traceless, rational in the dependent and independent variables, holomorphic in the monodromy exponents, with four Fuchsian singularities in the complex plane of the spectral parameter. Its only minor drawback is the presence of the apparent singularity which always exists in the scalar Lax pair.
    Année de publication : 2003
    Revue : J. Nonlinear Math. Phys. 10 107-118 (2003)
    conférence : in: Proceedings of Symmetries and Integrability of Difference Equations (SIDE V, 2002) ; Giens, France ; 2002-06-21 / 2002-06-26
    DOI : 10.2991/jnmp.2003.10.Supplement 2.10
    Keywords : Sixieme equation de Painleve; Paire de Lax; Discetisation
    Langue : Anglais
    NB : 10, Supp. 2, 107-118 (2003)
    Editeurs : Nijhoff F.W., Suris Y.B., Viallet C.

    Fichier(s) à télécharger :
  • paper.pdf
  • 10lig.pdf

  • On reductions of some KDV-type systems and their link to the quartic Henon-Heiles Hamiltonian

    Verhoeven C. (Tena)
    Musette M. (Tena)
    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Abstract:
    A few 2 + 1-dimensional equations belonging to the KP and modi- fied KP hierarchies are shown to be sufficient to provide a unified picture of all the integrable cases of the cubic and quartic HénonâHeiles Hamiltonians.
    Année de publication : 2006
    chapitre de livre : in: Proceedings of the NATO Advanced Research Workshop on Bilinear Integrable Systems: from Classical to Quantum, Continuous to Discrete
    Maison d'édition : Springer-Verlag, Berlin, 2006
    conférence invité : in: Proceedings of the NATO Advanced Research Workshop : Proceedings of the NATO Advanced Research Workshop in: Proceedings of the NATO Advanced Research Workshop on Bilinear Integrable Systems: from : from in: Proceedings of the NATO Advanced Re ; Isola d'Elba, Italy ; 2002-09-15 / 2002-09-19
    DOI : 10.1007/978-1-4020-3503-6_30
    Preprint : arXiv:nlin.SI/0405034
    Keywords : Sparation de variables; Fonctions hyperelliptiques; Transformations de Backlund
    Langue : Anglais
    Editeurs : Faddeev L., Lambert F.J., Van Moerbeke P.L.J.

    Fichier(s) à télécharger :
  • paper.pdf
  • 10lig.pdf
  • publi.pdf
  • ElbaVMC.pdf

  • General solution for Hamiltonians with extended cubic and quartic potentials

    Verhoeven C. (Tena)
    Musette M. (Tena)
    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Année de publication : 2003
    Revue : Theor. Math. Phys. 134 128-138 (2003)
    conférence : in: Proceedings of the XVth Nonlinear Evolution Equations and Dynamical Systems EuroConference (NEEDS 2001) ; Cambridge, UK ; 2001-07-24 / 2001-07-31
    Preprint : arXiv:nlin.SI/0301011
    PACS : 45.20.Jj, 05.45.Yv
    Keywords : Hnon-Heiles, Hamiltonian systems, Separation of variables, Nonlinear equations, Hyperelliptic functions, Soliton equations
    Langue : Anglais
    NB : 134, 128-138 (2003) [Translated from Teoret. Mat. Fiz. 134, 148-159 (2003)]
    Editeurs : Bruschi M., Calogero F., Mikhailov A.V., Santini P.M.

    Fichier(s) à télécharger :
  • paper.pdf
  • 10lig.pdf
  • publi.pdf
  • 0301011.pdf

  • Sur la solution analytique generale d'une equation differentielle chaotique du troisieme ordre

    Yee T.-L. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Musette M. (Tena)
    Abstract:
    Even if it is nonintegrable, a differential equation may nevertheless admit particular solutions which are globally analytic. On the example of the dynamical system of Kuramoto and Sivashinsky, which is generically chaotic and presents a high physical interest, we review various methods, all based on the structure of singularities, allowing us to characterize the analytic solution which depends on the largest possible number of constants of integration.
    Année de publication : 2003
    chapitre de livre : in: From Combinatorics to Dynamical Systems. Journees de Calcul Formel
    Maison d'édition : de Gruyter, Berlin
    conférence invité : in: From Combinatorics to Dynamical Systems. Journ'ees de Calcul : From Combinatorics to Dynamical Systems. Journ'ees de Calcul in: From Combinatorics to Dynamical Systems. Journ'ees de Calcul Formel ; Strasbourg, France ; 2002-03-22 / 2002-03-23
    Preprint : arXiv:nlin.PS/0302056
    PACS : 02.30.-f, 02.60.-x, 02.70.-c, 05.45.+b, 42.65.-k, 47.27.-i, 82.40.-g
    Keywords : Ondes solitaires; Equations de Briot et Bouquet; Nevanlinna; Algorithme LLL; Equation de Kuramoto et Sivashinsky; Equation de Ginzburg et Landau complexe Cubique unidimensionnelle; Genre; Troncature
    Langue : Français
    NB : 3, 195-212 (2003)
    Editeurs : Fauvet F., Mitschi C.

    Fichier(s) à télécharger :
  • paper.pdf
  • 10lig.pdf
  • publi.pdf
  • Strasbourg.pdf

  • A Truncation for Obtaining all the First Degree Birational Transformations of the Painleve Transcendents

    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Musette M. (Dienst Theoretische Natuurkunde, Pleinlaan 2, B-1050 Brussel)
    Abstract:
    A birational transformation is one which leaves invariant an ordinary differential equation, only changing its parameters. We first recall the consistent truncation which has allowed us to obtain the first degree birational transformation of Okamoto for the master Painleve equation P6. Then we improve it by adding a preliminary step, which is to find all the Riccati subequations of the considered Pn before performing the truncation. We discuss in some detail the main novelties of our method, taking as an example the simplest Painleve equation for that purpose, P2. Finally, we apply the method to P5 and obtain its two inequivalent first degree birational transformations.
    Année de publication : 2002
    Revue : J. Nonlinear Math. Phys. 9 14-28 (2002)
    conférence invité : Recent Advances in Integrable Systems: Proceedings of the Special Session on Integrable Systems of the First Joint International Meeting and the American Mathematical Society and the Hong-Kong Mathematical Society ; Hong-Kong, China ; 2000-12-13 / 2000-12-16
    Preprint : arXiv:nlin.SI/0110031
    Lien : http://www.sm.luth.se/~norbert/home_journal/hongkong00_elec.html
    PACS : 02.30.+g
    Keywords : Painleve equations, birational transformation, contiguity relation, Schlesinger transformation, singular manifold method, truncation.
    Langue : Anglais
    NB : 9, Suppl. 1, 14-28 (2002)
    Editeurs : Hu J., Ma W.X., Olver P.J., Yan M.

    Fichier(s) à télécharger :
  • paper.pdf
  • 0110031.pdf
  • 10lig.pdf
  • publi.pdf

  • First-degree birational transformations of the Painleve equations and their contiguity relations

    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Musette M. (Dienst Theoretische Natuurkunde, Vrije Universiteit Brussel Pleinlaan 2, B-1050 Bruxelles, BELGIQUE)
    Abstract:
    We present a consistent truncation, allowing us to obtain the first degree birational transformation found by Okamoto for the sixth Painlev'e equation. The discrete equation arising from its contiguity relation is then just the sum of six simple poles. An algebraic solution is presented, which is equivalent to but simpler than the Umemura solution. Finally, the well known confluence provides a unified picture of all first degree birational transformations for the lower Painlev'e equations, ranging them in two distinct sequences.
    Année de publication : 2001
    Revue : J. Phys. A 34 10507-10522 (2001)
    conférence invité : Symmetries and Integrability of Difference Equations (SIDE IV) ; Tokyo, Japan ; 2000-11-27 / 2000-12-01
    Preprint : arXiv:nlin.SI/0110028
    Lien : http://stacks.iop.org/JPhysA/34/10507
    PACS : 02.30.+g
    Keywords : Painlev equations, birational transformation, contiguity relation, singular manifold method, truncation
    Numéro Exterieur : hal-00121229
    Langue : Anglais
    NB : 34, 10507-10522 (2001)

    Fichier(s) à télécharger :
  • paper.pdf
  • 10lig.pdf
  • publi.pdf
  • 0110028.pdf

  • Backlund transformations from Painleve analysis

    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Musette M. (Dienst Theoretische Natuurkunde, Vrije Universiteit Brussel, Pleinlaan 2, B-1050 Brussels)
    Abstract:
    Année de publication : 2001
    Revue : Glasgow Math. J. 43A 9-21 (2001)
    conférence : Integrable systems: linear and nonlinear dynamics ; Islay, Scotland ; 1999-07-19 / 1999-07-24
    PACS : 02.90.+p,03.40.Kf
    Keywords : Backlund transformations, Painleve analysis
    Langue : Anglais
    NB : 43A, 9-21 (2001)
    Editeurs : Athorne C., Gilson C., Nimmo J.

    Fichier(s) à télécharger :
  • paper.pdf

  • Backlund transformation and non linear superposition formula of the Kaup--Kupershmidt and Tzitzeica equations

    Musette M. (Dienst Theoretische Natuurkunde, Vrije Universiteit Brussel Pleinlaan 2, B-1050 Brussels, BELGIQUE)
    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Verhoeven C. (Dienst Theoretische Natuurkunde, Vrije Universiteit Brussel Pleinlaan 2, B-1050 Brussels, BELGIQUE)
    Abstract:
    Année de publication : 2000
    chapitre de livre : Backlund and Darboux Transformations: The Geometry of Soliton Theory, AARMS-CRM Workshop
    Maison d'édition : American Mathematical Society, Providence, RI. USA
    conférence : Backlund and Darboux Transformations: The Backlund and Darboux Transformations: The Geometry of Soliton Theory, AARMS-CRM Workshop ; Halifax, Scotland ; 1999-06-05 / 1999-06-09
    PACS : 02.90.+p,03.40.Kf
    Keywords : Bcklund transformation, Tzitzica equation, Painlev analysis
    Langue : Anglais
    Editeurs : Coley A., Levi D., Milson R., Rogers C., Winternits P.

    On the solitary wave of two coupled nonintegrable Ginzburg-Landau equations

    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Musette M. (Dienst Theoretische Natuurkunde, Vrije Universiteit Brussel, Pleinlaan 2, B-1050 Bruxelles)
    Année de publication : 2000
    chapitre de livre : Nonlinear Integrability and all that: Twenty Years After NEEDS '79
    Maison d'édition : World Scientific, Singapore, 2000
    Pages : pp. 382-388
    Communication
    Keywords : Complex Ginzburg-Landau equation, exact solution
    Langue : Anglais
    Editeurs : Boiti M., Martina L., Pempinelli F., Prinari B., Soliani G.

    Fichier(s) à télécharger :
  • paper.pdf
  • 10lig.pdf

  • Perturbative methods for the Painleve test

    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Abstract:
    There exist many situations where an ordinary differential equation admits a movable critical singularity which the test of Kowalevski and Gambier fails to detect. Some possible reasons are: existence of negative Fuchs indices, insufficient number of Fuchs indices, multiple family, absence of an algebraic leading order. Mainly giving examples, we present the methods which answer all these questions. They are all based on the theorem of perturbations of Poincar'e and computerizable.
    Année de publication : 2000
    chapitre de livre : in Proceedings of the International Conference on Nonlinear Dynamics: Integrability and Chaos
    Maison d'édition : New Delhi, 2000
    Pages : pp. 117-126
    conférence invité : in Proceedings of the International Conference on Nonlinear in Proceedings of the International Conference on Nonlinear Dynamics: Integrability and Chaos : Integrability and Chaos ; Tiruchirapalli, India ; 1998-02-12 / 1998-02-16
    Preprint : arXiv:solv-int/9812007
    Langue : Anglais
    Editeurs : Daniel M., Ramizhamani K.M., Sahadevan R.

    Fichier(s) à télécharger :
  • paper.pdf
  • s048_txt.pdf
  • 10lig.pdf
  • publi.pdf

  • Various truncations in Painleve analysis of Partial Differential Equations

    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Abstract:
    The "truncation procedure" initiated by Weiss et al. is best understood as a Darboux transformation. If it leads to the Lax pair of the PDE under study, the Backlund transformation follows by an elimination, thus proving the integrability. We present the state of the art of this powerful technique. The easy situations were all handled by the WTC one-family truncation and its homographically invariant version. An updated version of this method has been recently developed, which is now able to handle the Kaup-Kupershmidt and Tzitzeica equations. It incorporates a new feature, namely the distinction between two entire functions usually mingled, which are shown to be linked by formulae established by Gambier for his classification.
    Année de publication : 2000
    chapitre de livre : in Proceedings of the International Conference on Nonlinear Dynamics: Integrability and Chaos
    Maison d'édition : New Delhi, 2000
    Pages : pp. 103-116
    conférence invité : in Proceedings of the International Conference on Nonlinear in Proceedings of the International Conference on Nonlinear Dynamics: Integrability and Chaos : Integrability and Chaos ; Tiruchirapalli, India ; 1998-02-12 / 1998-02-16
    Preprint : arXiv:solv-int/9812008
    Langue : Anglais
    Editeurs : Daniel M., Ramizhamani K.M., Sahadevan R.

    Fichier(s) à télécharger :
  • s047_txt.pdf
  • paper.pdf
  • 10lig.pdf
  • publi.pdf

  • Exact solutions of nonlinear wave equations by singularity methods

    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Année de publication : 1998
    chapitre de livre : Waves and stability in continuous media (WASCOM IX)
    conférence invité : Waves and stability in continuous media (WASCOM IX) ; Bari, Italia ; 1997-10-06 / 1997-10-11
    PACS : 02.90.+p,03.40.Kf
    Keywords : Exact solutions, nonperturbative methods, Painlev analysis
    Langue : Anglais
    NB : 57, 165-175 (1998) [Suppl.]
    Editeurs : Maiellaro M., Rionero S.

    Fichier(s) à télécharger :
  • paper.pdf
  • 10lig.pdf

  • Towards second order Lax pairs to discrete Painleve equations of first degree

    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Musette M. (Dienst Theoretische Natuurkunde, Vrije Universiteit Brussel, B-1050 Brussel, BELGIQUE)
    Abstract:
    We investigate the question of finding discrete Lax pairs for the six discrete Painlev'e equations (Pn). The choice we make is to discretize the pairs of Garnier, once converted to matricial form.
    Année de publication : 2000
    Revue : Chaos 11 41-52 (2000)
    conférence : Proceedings of Brussels Meeting II: Integrability and Chaos in Discrete Systems ; Brussels, Belgium ; 1997-07-02 / 1997-07-06
    Preprint : arXiv:solv-int/9803013
    PACS : 02.30.Ks, 02.90+p, 05.50.+q
    Keywords : Painleve equations, discrete Painleve equations, Lax pairs, discrete Lax pairs
    Langue : Anglais
    NB : 11, 41-52 (2000)
    Editeurs : Antoniou I., Lambert F.

    Fichier(s) à télécharger :
  • paper.pdf
  • 10lig.pdf
  • s018_txt.pdf
  • publi.pdf

  • Rules of discretization for Painleve equations, theory of nonlinear special functions: The Painleve transcendents

    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Musette M. (Dienst Theorietische Natuurkunde, Vrije Universiteit Brussel, B-1050 Brussel, BELGIQUE)
    Abstract:
    The discrete Painlev'e property is precisely defined, and basic discretization rules to preserve it are stated. The discrete Painlev'e test is enriched with a new method which perturbs the continuum limit and generates infinitely many no-log conditions. A general, direct method is provided to search for discrete Lax pairs.
    Année de publication : 1998
    chapitre de livre : Theory of Nonlinear Special Functions: the Painlev\\ Transcendents
    Maison d'édition : Springer-Verlag, Berlin, 1998
    Pages : 20 pp.
    conférence : Theory of Nonlinear Special Functions: the : the Theory of Nonlinear Special Functions: the Painlev Transcendents ; Montreal, Canada ; 1996-05-13 / 1996-05-17
    Preprint : arXiv:solv-int/9803014
    PACS : 02.30.Ks, 02.90+p, 05.50.+q
    Langue : Anglais
    Editeurs : Vinet L., Winternitz P.

    Fichier(s) à télécharger :
  • s075_txt.pdf
  • paper.pdf
  • 10lig.pdf
  • publi.pdf

  • Non-Fuchsian Painleve test

    Musette M. (Dienst Theoretische Natuurkunde, Vrije Universiteit Brussel B-1050 Brussel, Belgium)
    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Abstract:
    Année de publication : 1995
    chapitre de livre : in: Proceedings of the Workshop on Nonlinear Physics. Theory and Experiment
    Maison d'édition : World Scientific, Singapore, 1996
    Pages : pp. 225-232
    conférence : in: Proceedings of the Workshop on Nonlinear Physics. : Proceedings of the Workshop on Nonlinear Physics. in: Proceedings of the Workshop on Nonlinear Physics. Theory and Experiment ; Gallipoli, Italy ; 1995-06-29 / 1995-07-07
    Langue : Anglais
    Editeurs : Alfinito E., Boiti M., Martina L., Pempinelii F.

    Fichier(s) à télécharger :
  • paper.pdf
  • s057_txt.pdf
  • 10lig.pdf
  • publi.pdf

  • Beyond the two-singular manifold method

    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Musette M. (Dienst Theoretische Natuurkunde, Vrije Universiteit Brussel, B-1050 Brussel, Belgium)
    Année de publication : 1996
    chapitre de livre : in: Proceedings of the Workshop on Nonlinear Physics, Theory and Experiment
    Maison d'édition : World Scientific, Singapore, 1996
    conférence : in: Proceedings of the Workshop on : Proceedings of the Workshop on in: Proceedings of the Workshop on Nonlinear Physics, Theory and Experiment ; Gallipoli, Lecce, Italy ; 1995-06-29 / 1995-07-07
    Langue : Anglais

    Fichier(s) à télécharger :
  • paper.pdf
  • s056_txt.pdf
  • 10lig.pdf
  • publi.pdf

  • Exact solutions to the complex Ginzburg-Landau equation of non-linear optics

    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Musette M. (Dienst Theoretische Natuurkunde, Vrije Universiteit Brussel, Pleinlaan 2, B-1050 Brussel, BELGIUM)
    Année de publication : 2000
    Revue : Pure Appl. Opt. 4 315-320 (2000)
    conférence : Cost Workshop 94 Optical Telecommunications ; Nice, France ; 1994-04-17 / 1994-04-21
    Langue : Anglais
    NB : 4, 315-320 (1995)

    Fichier(s) à télécharger :
  • paper.pdf

  • Riccati pseudopotential of AKNS two-family NLPDEs by Painleve analysis

    Musette M. (Dienst Theoretische Natuurkunde Vrije Universiteit Brussel B-1050 Brussel, BELGIUM)
    Conte R. (SPHT, CEA/Saclay F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Abstract:
    Finding the Bäcklund transformation from the singularity structure is only impossible with the method of Weiss if the PDE has two families of singularities with opposite principal parts, such as the modified KdV and sine-Gordon equations. For such PDEs, we first consider the truncation with one manifold, derive the Darboux transformation (DT), and show that it involves the two entire functions associated with each family. Their ratio is then assumed to satisfy the most general Riccati system. This hypothesis, combined with the DT, generates a very small number of determining equations, admitting a unique solution, equivalent to the matricial Lax pair by the usual linearization of the Riccati system.
    Année de publication : 1994
    Revue : Theor. Math. Phys. 99 478-486 (1994)
    conférence : NEEDS'93 ; Gallipoli, Italy ; 1993-09-03 / 1993-09-12
    DOI : 10.1007/BF01017061
    Langue : Anglais
    NB : 99, 478-486 (1994) [en russe]; Transl.: Theor. Math. Phys. 99, 738-744 (1994)

    Fichier(s) à télécharger :
  • paper.pdf

  • Exact solutions to the partially integrable Eckhaus equation

    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Musette M. (Dienst Theoretische Natuurkunde Vrije Universiteit Brussel B-1050 Brussel, BELGIUM)
    Année de publication : 1994
    Revue : Teor. Mat. Fiz. 99 226-233 (1994)
    conférence : NEEDS'93 ; Gallipoli, Italy ; 1993-09-03 / 1993-09-12
    Langue : Anglais
    NB : 99, 226-233 (1994). Transl.: Theor. Math. Phys. 99, 543-548 (1994)

    Fichier(s) à télécharger :
  • paper.pdf
  • 10lig.pdf

  • Chaos and Complexity

    Trân Thanh Vân J. ()
    Bergé P. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Dubois M. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Année de publication : 1995
    livre
    Maison d'édition : Editions Frontires, Gif-sur-Yvette, 1995
    Pages : xviii, 345 pp.
    organisateur : Proceedings of the XXII International Meeting on Fundamental Physics. Fifth Rencontres de Blois. Colloque Interdisciplinaire du Comit National de la Recherche Scientifique ; Chteau de Blois, France ; 1993-06-21 / 1993-06-26
    Langue : Anglais

    Fichier(s) à télécharger :
  • paper.pdf
  • 10lig.pdf

  • A perturbative extension of the Painleve test

    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Fordy A.P. (University of Leeds, U.K.)
    Pickering A. (University of Leeds, U.K.)
    Abstract:
    Année de publication : 1993
    chapitre de livre : in: Proceedings of the NATO Advanced Research Workshop Applications of Analytic and Geometric Methods to Nonlinear Differential Equations
    Maison d'édition : Kluwer, Dordrecht, 1993
    conférence : in: Proceedings of the NATO Advanced Research Workshop : Proceedings of the NATO Advanced Research Workshop in: Proceedings of the NATO Advanced Research Workshop Applications of Analytic and Geometric Methods in: Proceedings of the NATO Advanced ; Exeter, UK
    Langue : Anglais
    NB : 413, 271-280 (1993)
    Editeurs : Clarkson P.A.

    Perturbative Painleve analysis

    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Fordy A.P. (University of Leeds, UK)
    Pickering A. (University of Leeds, UK)
    Abstract:
    Année de publication : 1992
    chapitre de livre : in: Proceedings of a NATO Advanced Study Institute in honour of Alwyn Scotts 60th birthday. Future Directions of Nonlinear Dynamics in Physical and Biological Systems
    Maison d'édition : Plenum Press, Ney York
    conférence : in: Proceedings of a NATO Advanced Study Institute in honour of : Proceedings of a NATO Advanced Study Institute in honour of in: Proceedings of a NATO Advanced Study Institute in honour of Alwyn Scott's 60th birthday. in: Proceedings of a NATO A ; Lyngby, Denmark
    Numéro Exterieur : Zbl.794.34011
    Langue : Anglais
    NB : 312, 1-5 (1993)
    Editeurs : Christiansen P.L., Eilbeck J.C., Parmentier R.D.

    Explicit solutions of the generalized Ginzburg-Landau equation from linear systems

    Musette M. (University of Brussel, Belgium)
    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Année de publication : 1992
    chapitre de livre : Nonlinear Evolution Equations and Dynamical Systems
    Maison d'édition : World Scientific, 1992
    conférence : Nonlinear Evolution Equations and Dynamical Systems ; Dubna, Russia
    Langue : Anglais
    Editeurs : Makhankov V.G., Pashaev O.K., Puzynin I.

    Identity of Fuchs indices and Painleve resonances: new non-log conditions

    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Fordy A.P. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Pickering A. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Abstract:
    Année de publication : 1992
    chapitre de livre : Nonlinear Evolution Equations and Dynamical Systems
    Maison d'édition : World Scientific, 1992
    conférence : Nonlinear Evolution Equations and Dynamical Systems ; Dubna, Russia
    Langue : Anglais
    Editeurs : Makhankov V.G., Pashaev O.K., Puzynin I.

    Exact solutions to the complex Ginzburg-Landau equation from a linear system

    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Musette M. (Vrije Universiteit Brussel, Belgium)
    Année de publication : 1993
    chapitre de livre : in: Proceedings of the NATO Advanced Research Workshop Applications of Analytic and Geometric Methods to Nonlinear Differential Equations
    Maison d'édition : Kluwer, Dordrecht
    conférence : in: Proceedings of the NATO Advanced Research Workshop : Proceedings of the NATO Advanced Research Workshop in: Proceedings of the NATO Advanced Research Workshop Applications of Analytic and Geometric Methods in: Proceedings of the NATO Advanced ; Exeter, UK
    Langue : Anglais
    NB : 413, 281-286 (1993)
    Editeurs : Clarkson P.A.

    A Fuchs extension to the Painleve test

    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Fordy A.P. (University of Leeds, UK)
    Pickering A. (University of Leeds, UK)
    Abstract:
    Année de publication : 1992
    chapitre de livre : III Potsdam International Workshop on Nonlinear Processes in Physics
    Maison d'édition : Springer-Verlag, 1992
    conférence : III Potsdam International Workshop on III Potsdam International Workshop on Nonlinear Processes in Physics ; Potsdam, NY, USA
    Langue : Anglais
    NB : pp. 35-44
    Editeurs : Fokas A., Kaup D.J., Newell A.C., Zakharov V.E.

    Solitary waves and Lax pairs from polynomial expansions of nonlinear differential equations

    Musette M. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Conte R. (~)
    Année de publication : 1992
    chapitre de livre : Nonlinear Evolution Equations and Dynamical Systems
    Maison d'édition : World Scientific, 1992
    conférence : Nonlinear Evolution Equations and Dynamical Systems ; Gallipoli, Italy
    Langue : Anglais
    NB : pp. 161-170
    Editeurs : Boiti M., Martina L., Pempinelli F.

    The test of negative integer indices in Painleve analysis of NLPDE

    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Abstract:
    Année de publication : 1992
    chapitre de livre : Nonlinear Evolution Equations and Dynamical Systems
    Maison d'édition : World Scientific, 1992
    conférence : Nonlinear Evolution Equations and Dynamical Systems ; Gallipoli, Italy
    Langue : Anglais
    NB : pp. 269-278
    Editeurs : Boiti M., Martina L., Pempinelli F.

    Towards the equivalence between integrability and Painleve test for partial differential equations

    Conte R. (~)
    Abstract:
    Année de publication : 1991
    chapitre de livre : Nonlinear and Chaotic Phenomena in Plasmas, Solids and Fluids
    Maison d'édition : World Scientific, 1991
    conférence : Nonlinear and Chaotic Phenomena in Plasmas, Solids and Fluids ; Edmonton, Canada
    Langue : Anglais
    NB : pp. 94-101
    Editeurs : Rozmus W., Tuszynski J.A.

    Unification of PDE and ODE versions of Painleve analysis into a single invariant version

    Conte R. (~)
    Abstract:
    Année de publication : 1992
    chapitre de livre : in: Proceedings of the NATO Advanced Research Workshop Painleve Transcendents, their Asymptotics and Physical Applications
    Maison d'édition : Plenum Press, New York
    conférence : in: Proceedings of the NATO Advanced Research Workshop : Proceedings of the NATO Advanced Research Workshop in: Proceedings of the NATO Advanced Research Workshop Painlev Transcendents, their Asymptotics and Physical in: Proceedings of the NAT ; Sainte-Adle, Qubec, Canada
    Langue : Anglais
    NB : 278, 125-144 (1992)
    Editeurs : Levi D., Winternitz P.

    Partially integrable evolution equations in physics

    Conte R. (~)
    Boccara N. (~)
    Année de publication : 1990
    Revue : NATO ASI Series C 310 xvii (1990)
    livre
    Maison d'édition : Kluwer Academic Publishers, Dordrecht
    organisateur : in: Procedings of the NATO Advanced Study Institute on Partially Integrable Nonlinear Evolution Equations and their Applications ; Les Houches, France
    Langue : Anglais
    NB : 310, p. xvii (605)

    The homographic invariance of PDE Painleve analysis

    Conte R. (~)
    Abstract:
    Année de publication : 1990
    chapitre de livre : Partially Integrable Evolution Equations in Physics
    Maison d'édition : Kluwer Academic Publishers
    conférence : Partially Integrable Evolution Equations in Physics ; Les Houches, France
    Langue : Anglais
    NB : 310, 577-578 (1990)
    Editeurs : Boccara N., Conte R.

    Painleve singular manifold equation and integrability

    Conte R. (~)
    Abstract:
    Année de publication : 1990
    chapitre de livre : in: Proceedings of the Multicentennials on Meeting on Inverse Problems. Inverse Methods in Action, Inverse Problems and Theoretical Imaging
    Maison d'édition : Springer-Verlag, Berlin
    conférence : in: Proceedings of the Multicentennials on Meeting on Inverse : Proceedings of the Multicentennials on Meeting on Inverse in: Proceedings of the Multicentennials on Meeting on Inverse Problems. Inverse Methods in Action, Inverse Problems and in: ; Montpellier, France
    Langue : Anglais
    NB : 264, 497-504 (1990)
    Editeurs : Sabatier P.C.

    Painleve analysis of nonlinear PDE'S and related topics: a computer algebra program

    Conte R. (~)
    Abstract:
    Année de publication : 1990
    chapitre de livre : Workshop on Computer Algebra and Differential Equations
    Maison d'édition : Academic Press, 1990
    conférence : Workshop on Computer Algebra and Differential Equations ; Grenoble, France
    Langue : Anglais
    NB : p. 219
    Editeurs : Tournier E.

    Painleve analysis and Backlund transformation of the nonintegrable KPP partial differential equation

    Conte R. (~)
    Abstract:
    Année de publication : 1990
    chapitre de livre : Workhop Nonlinear Evolution Equations: Integrability and Spectral Methods
    Maison d'édition : Manchester University Press
    conférence : Workhop Nonlinear Workhop Nonlinear Evolution Equations: Integrability and Spectral Methods : Integrability and Spectral Methods ; Como, Italy
    Numéro Exterieur : Zbl.724.35025 ; Zbl.703.00014
    Langue : Anglais
    NB : pp. 187-192 (1990)
    Editeurs : Degasperis A., Fordy A.P., Lakshmanan M.

    Solitary waves, Backlund transformation from the Painleve analysis in the Kuramoto-Sivashinsky equation

    Conte R. (~)
    Musette M. (~)
    Abstract:
    Année de publication : 1988
    chapitre de livre : in: Proceedings of the 16th Workshop on interdisciplinary study of inverse problems. R.C.P. 264 Meeting. Some Topics on Inverse Problems
    Maison d'édition : World Scientific, Singapore, 1988
    conférence : in: Proceedings of the 16th Workshop on interdisciplinary : Proceedings of the 16th Workshop on interdisciplinary in: Proceedings of the 16th Workshop on interdisciplinary study of inverse problems. R.C.P. 264 Meeting. in: Proceedings of the 16th ; Montpellier, France
    Langue : Anglais
    NB : pp. 65-78
    Editeurs : Sabatier P.C.

    Lyapunov exponents of experimental systems

    Conte R. (~)
    Dubois M. (~)
    Année de publication : 1988
    chapitre de livre : in: Proceedings of the IVth Workshop on Nonlinear Evolution Equations and Dynamical Systems. Nonlinear Evolutions
    Maison d'édition : World Scientific, 1988
    conférence : in: Proceedings of the IVth Workshop on Nonlinear Evolution : Proceedings of the IVth Workshop on Nonlinear Evolution in: Proceedings of the IVth Workshop on Nonlinear Evolution Equations and Dynamical Systems. Nonlinear Evolutions ; Balaruc-les-Bains, France
    Langue : Anglais
    NB : pp. 767-780
    Editeurs : Leon J.J.P

    Order as a consequence of disorder in frustrated Ising models

    Bidaux R. (~)
    Carton J.P. (~)
    Conte R. (~)
    Villain J. (~)
    Année de publication : 1981
    chapitre de livre : Disordered Systems and Localization
    Maison d'édition : Springer-Verlag, Berlin
    conférence : Disordered Systems and Localization ; Rome, Italy
    Langue : Anglais
    NB : 149, 161-165 (1981)
    Editeurs : Castellani C., Di Castro C., Peliti L.

    Frustration effects in 2D regular Ising models

    André G. (~)
    Bidaux R. (~)
    Carton J.P. (~)
    Conte R. (~)
    De Seze L. (~)
    Année de publication : 1979
    Revue : J. Appl. Phys. 50 7345-7347 (1979)
    conférence : in: Proceedings of the Second Joint International Magnetics and Magnetism and Magnetic Materials Conference (INTERMAG-MMM 1979) ; New York, USA
    Langue : Anglais
    NB : 50, 7345-7347 (1979)
    Editeurs : Janak J.F., O'Handley R.C.

    Magneto-elastic coupling by dipolar interactions: Spin orientation in MnO

    Bidaux R. (~)
    Conte R. (~)
    Nasser J.A. (~)
    Année de publication : 1979
    Revue : J. Appl. Phys. 50 1683-1684 (1979)
    conférence : in: Proceedings of the Twenty-Fourth Annual Conference on Magnetism and Magnetic Materials ; Cleveland, Ohio, USA
    Langue : Anglais
    NB : 50, 1683-1684 (1979)
    Editeurs : Becker J.J., Bonner J.C.

    Instabilite d'une nappe cylindrique de tourbillons

    Boccara N. (~)
    Conte R. (~)
    Sarma G. (~)
    Abstract:
    Année de publication : 1976
    Revue : J. Physique 37 C1 (1976)
    conférence : in: Exposes et Communications du Colloque de la Societe Francaise de Physique. Hydrodynamique Physique et Instabilites - Physical Hydrodynamics and Instabilities ; Dijon, France
    Langue : Français
    NB : 37, p. C1 (191-194)
    Editeurs : Martinet A.

    Theoretical determination of the order of a d-dimensional displacive phase transition

    Conte R. (~)
    Année de publication : 1974
    Revue : Ferroelectrics 7 389 (1974)
    conférence : 3rd International Conference on Ferroelectricity ; Edinburgh, Scotland
    Langue : Anglais
    NB : 7, p. 389 (1974)

    Etude de quelques proprietes magnetiques du thiospinelle MnCr_2S_4

    Plumier R. (~)
    Conte R. (~)
    Denis J. (~)
    Nauciel-Bloch M. (~)
    Abstract:
    Année de publication : 1971
    Revue : J. Physique 32 C1 (1971)
    conférence : in: Expos'es et communications de la 7eme Conference Internationale de Magnetisme ; Grenoble, France
    Langue : Français
    NB : 32, p. C1 (55-56)


    4 dans la catégorie Ouvrages

    The Painleve handbook

    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Musette M. (Tena)
    Abstract:
    Année de publication : 2009
    livre
    Maison d'édition : Springer-Verlag, Berlin, 2008
    PACS : 02.30.Hq,02.30.Jr,02.70.Bf
    Keywords : Painlev equations, singularity analysis, exact solutions
    Langue : Anglais

    Fichier(s) à télécharger :
  • paper.pdf
  • 10lig.pdf

  • Solitary waves of nonlinear nonintegrable equations

    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Musette M. (Tena)
    Année de publication : 2005
    Revue : Lect. Notes Phys. 661 373-406 (2005)
    chapitre de livre : Dissipative solitons
    Maison d'édition : Springer-Verlag, Berlin
    DOI : 10.1007/10928028_15
    Preprint : arXiv:nlin.PS/0407026
    Keywords : Solitary waves; Exact solutions; Elliptic functions; Truncation; Painlev test
    Numéro Exterieur : hal-00126534
    Langue : Anglais
    NB : 661, 373-406 (2005)
    Editeurs : Akhmediev N., Ankiewicz A.

    Fichier(s) à télécharger :
  • paper.pdf
  • 10lig.pdf
  • Akhmediev.pdf
  • publi.pdf

  • The Painleve methods

    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Musette M. (Dienst Theoretische Natuurkunde, Vrije Universiteit Brussel Pleinlaan 2, B-1050 Bruxelles, BELGIQUE)
    Abstract:
    Année de publication : 2003
    chapitre de livre : Classical and Quantum Nonlinear Integrable Systems: Theory and Applications
    Maison d'édition : Institute of Physics Publishing, Bristol, 2003
    Pages : 39-63
    Preprint : arXiv:nlin.SI/0211048
    PACS : 02.30.+g
    Keywords : Painleve property; Painleve test; Backlund transformation; Integrability
    Langue : Anglais
    Editeurs : Kundu A.

    Fichier(s) à télécharger :
  • 0211048.pdf
  • paper.pdf
  • 10lig.pdf
  • publi.pdf

  • A simple method to obtain first integrals of dynamical systems

    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Musette M. (Vrije Universiteit, Brussel, Belgium)
    Année de publication : 1991
    chapitre de livre : Solitons and Chaos
    Maison d'édition : Springer-Verlag, Berlin, 1991
    Langue : Anglais
    NB : pp. 125-128
    Editeurs : Antoniou I., Lambert F.J.


    6 dans la catégorie Cours

    Completeness of the cubic and quartic H\\énon-Heiles Hamiltonians

    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Musette M. (Tena)
    Verhoeven C. (Tena)
    Année de publication : 2005
    Revue : Theor. Math. Phys. 144 888-898 (2005)
    cours : Nonlinear Physics: Theory and Experiment. III ; Gallipoli, Italie ; 2004-06-24 / 2004-07-03
    DOI : 10.1007/s11232-005-0115-9
    Preprint : arXiv:nlin.SI/0507011
    PACS : 02.30.Hq, 03.40
    Keywords : Hnon-Heiles Hamiltonian; Painlev property; Hyperelliptic; Separation of variables
    Langue : Anglais
    NB : 144, 888-898 (2005); Teor. Mat. Fiz. 144, 14-25 (2005)
    Editeurs : Ablowitz M.J., Boiti M., Pempinelli F., Prinari B.

    Fichier(s) à télécharger :
  • paper.pdf
  • 0507011.pdf
  • 10lig.pdf
  • publi.pdf

  • Exact solutions of nonlinear partial differential equations by singularity analysis

    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Année de publication : 2003
    Revue : Lect. Notes Phys. 632 1-83 (2003)
    livre
    Maison d'édition : Springer-Verlag, Berlin
    cours : in: Lectures Given at the CIME Summer School on Direct and Inverse Methods in Nonlinear Evolution Equations ; Cetraro, Italy ; 1999-09-05 / 1999-09-12
    DOI : 10.1007/b13714
    Preprint : arXiv:nlin.SI/0009024
    PACS : 02.90.+p,03.40.Kf
    Keywords : Exact solutions, nonperturbative methods, Painlev analysis
    Langue : Anglais
    NB : 632, 1-83 (2003)
    Editeurs : Greco A.

    Fichier(s) à télécharger :
  • paper.pdf
  • publi.pdf
  • conte.pdf

  • The Painleve approach to nonlinear ordinary differential equations

    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Abstract:
    Année de publication : 1999
    Revue : CRM Series Math. Phys. (1999)
    livre
    Maison d'édition : Springer-Verlag, Berlin
    cours : in: Proceedings of the Cargese School Painleve, un siecle apres. The Painleve property, one century later ; Cargese, France ; 1996-06-03 / 1996-06-22
    Preprint : arXiv:solv-int/9710020
    Langue : Anglais
    NB : pp. 77-180 (1999)

    Fichier(s) à télécharger :
  • 9710020.pdf
  • paper.pdf
  • 10lig.pdf
  • publi.pdf

  • Preface

    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Année de publication : 1999
    Revue : CRM Series Math. Phys. (1999)
    livre
    Maison d'édition : Springer-Verlag, New York
    Pages : 810 pp.
    cours : Proceedings of the Cargse School: La proprit de Painlev, un sicle aprs. The Painlev Property: One Century Later ; Cargse, France ; 1996-06-03 / 1996-06-22
    Langue : Anglais
    NB : pp. xv-xvii (1999)

    Fichier(s) à télécharger :
  • paper.pdf
  • 10lig.pdf

  • Singularities of differential equations and integrability

    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Année de publication : 1994
    livre
    Maison d'édition : Editions Frontires, Gif-sur-Yvette, 1994
    Pages : pp. 49-143
    cours : in: Proceedings of the Third Workshop in Astronomy and Astrophysics. An introduction to methods of complex analysis and geometry for classical mechanics and non-linear waves (Cham93) ; Chamonix, France ; 1993-02-01 / 1993-02-06
    Langue : Anglais
    Editeurs : Benest D., Froeschle C.

    Fichier(s) à télécharger :
  • paper.pdf
  • 10lig.pdf

  • Les langages formels

    Conte R. (~)
    Année de publication : 1980
    cours : Journes Chimie Physique et Informatique. Chimie Physique ; Saclay, France
    Langue : Français
    NB : pp. 94-101


    1 dans la catégorie Thse

    Etude d'ecoulements bidimensionnels tourbillonnaires : mouvement de trois ou quatre tourbillons ponctuels et de nappes tourbillonnaires

    Conte R. (~)
    Abstract:
    Année de publication : 1979
    thése
    soutenance de thése : Universite Paris VI
    Langue : Français


    0 dans la catégorie Sminaire


    5 dans la catégorie Misc

    General solution of the Henon-Heiles Hamiltonian system in the third integrable case

    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Musette M. (Dienst Theoretische Natuurkunde, Vrije Universiteit Brussel, B-1050 Brussel, BELGIQUE)
    Abstract:
    Année de publication : 1998
    Conférence - : 20th IUAP International Conference on Statistical Physics (StatPhys 20) ; UNESCO, La Sorbonne, Paris, France ; 1998-07-20 / 1998-07-24
    Langue : Anglais

    Fichier(s) à télécharger :
  • paper.pdf
  • 10lig.pdf

  • Analytic Proofs of Nonintegrability of the Bianchi IX Model

    Latifi A. (International Solvay Institutes of Physics and Chemistry Université libre de Bruxelles Campus Plaine CP 231, B-1050 Bruxelles, BELGIQUE)
    Musette M. (Dienst Theoretische Natuurkunde Vrije Universiteit Brussel Pleinlaan 2, B-1050 Brussel, BELGI\E)
    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Année de publication : 1994
    Conférence - : XIth International Congress of Mathematical Physics ; UNESCO, La Sorbonne, Paris, France ; 1994-07-18 / 1994-07-23
    Langue : Anglais
    Editeurs : Iagolnitzer D.

    Fichier(s) à télécharger :
  • paper.pdf
  • 10lig.pdf

  • Nonintegrability of the Bianchi IX model

    Latifi A. (International Solvay Institutes of Physics and Chemistry Université libre de Bruxelles Campus Plaine CP 231, B-1050 Bruxelles, BELGIQUE)
    Musette M. (Dienst Theoretische Natuurkunde Vrije Universiteit Brussel, Pleinlaan 2, B-1050 Brussel, BELGIQUE)
    Conte R. (DSM/IRAMIS/SPEC, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, FRANCE)
    Année de publication : 1995
    Revue : Physica D 87 70-72 (1995)
    Conférence - : NLS 94 ; Chernogolovka, Russia ; 1994-07-25 / 1994-08-03
    Langue : Anglais
    NB : 87, 70-72 (1995)

    Fichier(s) à télécharger :
  • paper.pdf
  • 10lig.pdf
  • publi.pdf
  • conte.pdf

  • Corrections to the Onsager critical temperature of the rectangular Ising model in the presence of next nearest neighbour interactions

    Bidaux R. (~)
    Conte R. (~)
    De Seze L. (~)
    Année de publication : 1985
    Conférence - : International Conference on Magnetism ; San Francisco, USA
    Langue : Anglais

    Sur une nouvelle methode de determination des fonctions harmoniques cubiques valable pour J quelconque

    Conte R. (~)
    Raynal J. (~)
    Soulié E. (~)
    Abstract:
    Année de publication : 1980
    Conférence - : Colloque P. Curie ; Paris, France
    Langue : Français

     

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