Stability investigation of quadratic systems with delay.
Stability of periodic waves in Hamiltonian PDEs
Partial differential equations endowed with a Hamiltonian structure, like the Korteweg–de Vries equation and many other more or less classical models, are known to admit rich families of periodic travelling waves. The stability theory for these waves is still in its infancy though. The issue has been tackled by various means. Of course, it is always possible to address stability from the spectral point of view. However, the link with nonlinear stability - in fact, orbital stability, since we are...
Stability of solitary wave solutions for equations of short and long dispersive waves.
Stability of solitary waves for derivative nonlinear Schrödinger equation
Structure theory for second order 2D superintegrable systems with 1-parameter potentials.
Supersymmetric representations and integrable fermionic extensions of the Burgers and Boussinesq equations.
Supersymmetry of affine Toda models as fermionic symmetry flows of the extended mkdv hierarchy.
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.