Lax integrable supersymmetric hierarchies on extended phase spaces.
Le problème de Cauchy pour des EDP semi-linéaires périodiques en variables d'espace
L’équation de Klein Gordon à données petites
Les équations d’Euler, des ondes et de Korteweg-de Vries comme limites asymptotiques de l’équation de Gross-Pitaevskii
Local analyticity in the time and space variables and the smoothing effect for the fifth-order KdV-type equation.
Local existence in time of small solutions to the Davey-Stewartson systems
Local solution for the Kadomtsev-Petviashvili equation with periodic conditions.
Local well-posedness for a higher order nonlinear Schrödinger equation in Sobolev spaces of negative indices.
Long time asymptotics of the Camassa–Holm equation on the half-line
We study the long-time behavior of solutions of the initial-boundary value (IBV) problem for the Camassa–Holm (CH) equation on the half-line . The paper continues our study of IBV problems for the CH equation, the key tool of which is the formulation and analysis of associated Riemann–Hilbert factorization problems. We specify the regions in the quarter space-time plane , having qualitatively different asymptotic pictures, and give the main terms of the asymptotics in terms of spectral data...
Long-time asymptotics of solutions to some nonlinear wave equations
In this paper, we survey some recent results on the asymptotic behavior, as time tends to infinity, of solutions to the Cauchy problems for the generalized Korteweg-de Vries-Burgers equation and the generalized Benjamin-Bona-Mahony-Burgers equation. The main results give higher-order terms of the asymptotic expansion of solutions.
Loop groups and equations of KdV type
Microscopic shocks in one dimensional driven systems
Minoration du temps d'existence pour l'équation de Klein-Gordon non-linéaire en dimension 1 d'espace
Modulation of the Camassa-Holm equation and reciprocal transformations
We derive the modulation equations (Whitham equations) for the Camassa-Holm (CH) equation. We show that the modulation equations are hyperbolic and admit a bi-Hamiltonian structure. Furthermore they are connected by a reciprocal transformation to the modulation equations of the first negative flow of the Korteweg de Vries (KdV) equation. The reciprocal transformation is generated by the Casimir of the second Poisson bracket of the KdV averaged flow. We show that the geometry...
Moving frames, Geometric Poisson brackets and the KdV-Schwarzian evolution of pure spinors
In this paper we describe a non-local moving frame along a curve of pure spinors in , and its associated basis of differential invariants. We show that the space of differential invariants of Schwarzian-type define a Poisson submanifold of the spinor Geometric Poisson brackets. The resulting restriction is given by a decoupled system of KdV Poisson structures. We define a generalization of the Schwarzian-KdV evolution for pure spinor curves and we prove that it induces a decoupled system of KdV...
Multicomponent Burgers and KP hierarchies, and solutions from a matrix linear system.
Multi-helicoidal Euclidean submanifolds of constant sectional curvature.
Nearly concentric Korteweg-de Vries equation and periodic traveling wave solution.
New exact solutions for the -dimensional Broer-Kaup-Kupershmidt equations.
New exact traveling wave solutions for compound KdV-Burgers equations in mathematical physics.