Real Hamiltonian forms of affine Toda models related to exceptional Lie algebras.
Reduction of infinite dimensional equations.
Restricted flows and the soliton equation with self-consistent sources.
Scalar-flat Kähler metrics with SU (2) symmetry.
Self-consistent-field method and -functional method on group manifold in soliton theory: a review and new results.
Singularity analysis and integrability of a Burgers-type system of Foursov.
Soliton and periodic wave solutions to the osmosis equation.
Solitons, peakons, and periodic cuspons of a generalized Degasperis-Procesi equation.
Solvability of the super KP equation and a generalization of the Birkhoff decomposition.
Some remarks on the KP system of the Camassa-Holm hierarchy.
Spectral curves, opers and integrable systems
Spectral invariants for coupled spin-oscillators
This text deals with inverse spectral theory in a semiclassical setting. Given a quantum system, the haunting question is “What interesting quantities can be discovered on the spectrum that can help to characterize the system ?” The general framework will be semiclassical analysis, and the issue is to recover the classical dynamics from the quantum spectrum. The coupling of a spin and an oscillator is a fundamental example in physics where some nontrivial explicit calculations can be done.
Spectrum and generation of solutions of the Toda lattice.
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.
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 .
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