Schrödinger equation

We consider the cubic Nonlinear Schrödinger equation in the plane with condition of modulus one at infinity. This model possesses traveling waves. We shall present two types of results of existence of (smooth) branches of traveling waves: a theoretical one obtained in collaboration with E. Pacherie for small speeds and numerical results obtained in collaboration with C. Sheid on the excited states for this model.

The Landau-Lifshitz equation gives account of the dynamics of magnetization in ferromagnets. The goal of this talk is to describe the rigorous derivation of two aymptotic regimes of this equation corresponding to the Sine-Gordon equation and the cubic Schrödinger equation. This talk is based on two papers in collaboration with André de Laire (University of Lille).