Implicit difference scheme for the numerical resolution of the Charney-Obukhov equation with variable coefficients.
Initial boundary value problem for the mKdV equation on a finite interval
We analyse an initial-boundary value problem for the mKdV equation on a finite interval by expressing the solution in terms of the solution of an associated matrix Riemann-Hilbert problem in the complex -plane. This RH problem is determined by certain spectral functions which are defined in terms of the initial-boundary values at and . We show that the spectral functions satisfy an algebraic “global relation” which express the implicit relation between all boundary values in terms of spectral...
Instability of the stationary solutions of generalized dissipative Boussinesq equation
In this work we study the generalized Boussinesq equation with a dissipation term. We show that, under suitable conditions, a global solution for the initial value problem exists. In addition, we derive sufficient conditions for the blow-up of the solution to the problem. Furthermore, the instability of the stationary solutions of this equation is established.
Integrability of the Bakirov system: a zero-curvature representation.
Integrable three-dimensional coupled nonlinear dynamical systems related to centrally extended operator Lie algebras and their Lax type three-linearization
The Hamiltonian representation for a hierarchy of Lax type equations on a dual space to the Lie algebra of integro-differential operators with matrix coefficients, extended by evolutions for eigenfunctions and adjoint eigenfunctions of the corresponding spectral problems, is obtained via some special Bäcklund transformation. The connection of this hierarchy with integrable by Lax two-dimensional Davey-Stewartson type systems is studied.
Integrals of Motion of Classical Lattice Sine-Gordon System
Interface cinétique / fluide : Un modèle simplifié
Internal modes of solitons and near-integrable highly-dispersive nonlinear systems.
Invariance of the Gibbs measure for the Benjamin–Ono equation
In this paper we consider the periodic Benjemin-Ono equation.We establish the invariance of the Gibbs measure associated to this equation, thus answering a question raised in Tzvetkov [28]. As an intermediate step, we also obtain a local well-posedness result in Besov-type spaces rougher than , extending the well-posedness result of Molinet [20].
Invariant measures and long-time behavior for the Benjamin-Ono equation
We summarize the main ideas in a series of papers ([20], [21], [22], [5]) devoted to the construction of invariant measures and to the long-time behavior of solutions of the periodic Benjamin-Ono equation.
Invariant measures for Burgers equation with stochastic forcing.
Isometric immersions of domains of Lobachevski space in Euclidean spaces