Sur le caractère bien posé des équations de Schrödinger non linéaires
Surfaces in three-dimensional Lie groups.
Symmetries in connection preserving deformations.
Symmetries of the nonlinear Schrödinger equation
Symmetries of the defocusing nonlinear Schrödinger equation are expressed in action-angle coordinates and characterized in terms of the periodic and Dirichlet spectrum of the associated Zakharov-Shabat system. Application: proof of the conjecture that the periodic spectrum of a Zakharov-Shabat operator is symmetric,i.e. for all , if and only if the sequence of gap lengths, , is symmetric with respect to .
Symmetry group analysis and invariant solutions of hydrodynamic-type systems.
Symmetry properties of a generalized Korteweg-de Vries equation and some explicit solutions.
Symplectic topology of integrable dynamical systems. Rough topological classification of classical cases of integrability in the dynamics of a heavy rigid body
Systèmes hamiltoniens complètement intégrables et déformations d'algèbres de Lie.
Some of the completely integrable Hamiltonian systems obtained through Adler-Kostant-Symes theorem rely on two distinct Lie algebra structures on the same underlying vector space. We study here the cases when two structures are linked together by deformations.
Systèmes intégrables à -corps sur la droite
Systems of Toda Type, Inverse Spectral Problems, and Representation Theory.
The algebraic Bethe Ansatz and vacuum vectors.
The Algebraic Integrability of Geodesic Flow on S0(4).
The algebro-geometric Toda hierarchy initial value problem for complex-valued initial data.
The Cauchy problem for the Gross–Pitaevskii equation
The complex geometry of the Kowalewski-Painlevé analysis.
The cubic Szegő equation
We consider the following Hamiltonian equation on the Hardy space on the circle,where is the Szegő projector. This equation can be seen as a toy model for totally non dispersive evolution equations. We display a Lax pair structure for this equation. We prove that it admits an infinite sequence of conservation laws in involution, and that it can be approximated by a sequence of finite dimensional completely integrable Hamiltonian systems. We establish several instability phenomena illustrating...
The equivalence between the Hamiltonian and Lagrangian formulations for the parametrization-invariant theories.
The family of isometric superconformal harmonic maps and the affine Toda equations.
The finite discrete KP hierarchy and the rational functions.
The four positive vortices problem : regions of chaotic behavior and the non-integrability