Large energy simple modes for a class of Kirchhoff equations.
Lax equation representation of certain completely integrable systems
Lax integrable supersymmetric hierarchies on extended phase spaces.
Level set structure of an integrable cellular automaton.
Lie symmetries and criticality of semilinear differential systems.
Lie-group analysis of radiative and magnetic field effects on free convection and mass transfer flow past a semi-infinite vertical flat plate.
Limit matrices for the Toda flow and periodic flags for loop groups.
Lindstedt series, ultraviolet divergences and Moser's theorem
Linear hamiltonian circle actions that generate minimal Hilbert bases
The orbit space of a linear Hamiltonian circle action and the reduced orbit space, at zero, are examples of singular Poisson spaces. The orbit space inherits the Poisson algebra of functions invariant under the linear circle action and the reduced orbit space inherits the Poisson algebra obtained by restricting the invariant functions to the reduced space. Both spaces reside inside smooth manifolds, which in turn inherit almost Poisson structures from the Poisson varieties. In this paper we consider...
Linearising two-dimensional integrable systems and the construction of action-angle variables.
Liouville integrability of geometric variational problems.
Local analyticity in the time and space variables and the smoothing effect for the fifth-order KdV-type equation.
Localized induction equation for stretched vortex filament.
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 dynamics for the one dimensional non linear Schrödinger equation
In this article, we first present the construction of Gibbs measures associated to nonlinear Schrödinger equations with harmonic potential. Then we show that the corresponding Cauchy problem is globally well-posed for rough initial conditions in a statistical set (the support of the measures). Finally, we prove that the Gibbs measures are indeed invariant by the flow of the equation. As a byproduct of our analysis, we give a global well-posedness and scattering result for the critical and super-critical...
Loop groups and equations of KdV type
Lyapunov center theorem for some nonlinear PDE's : a simple proof
Majorations affines du nombre de zéros d'intégrales abéliennes pour les hamiltoniens quartiques elliptiques
Manin matrices, quantum elliptic commutative families and characteristic polynomial of elliptic Gaudin model.
Mechanical analogy for the wave-particle: Helix on a vortex filament.