Branches of traveling waves for the Nonlinear Schrödinger equation

David Chiron
Laboratoyr J.A. Dieudonné, Université Côte d'Azur, Parc Valrose 06108 NICE Cedex 02, France
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.