Rentrée du Séminaire des doctorants

Ordre du jour :

-Présentation du laboratoire, de l'école doctorale MADIS et du labex CEMPI.

-Exposé de Patrick Popescu-Pampu : René Thom et la genèse des formes.

-Exposé de Erwan Le Quiniou : Exotic traveling waves for a nonlinear Shrödinger equation.

We consider a modified quasilinear version of the Gross-Pitaevskii equation. Intuitively this is a nonlinear Schrödinger equation where the terms involving spatial dervatives depend on the unknown function.
We also recquire the solutions to satisfy nonzero conditions at infinity. In this setting we classify particular solution of these PDEs—the traveling waves of finite energy—in terms of two parameters: the propagation speed of the wave and a real number measuring the importance of the quasilinear terms. Furthermore, we prove that some of these waves can be obtained by minimization of the energy at fixed momentum, and that they are orbitably stable.
The aim of this talk is to presents our results. We will discuss the properties of the admissible travelling wave profiles to conclude on a sketch of the proof for the orbital stability of some solutions.