# On a nonlinear Schrödinger equation for nucleons

 Orateur: ROTA NODARI Simona Localisation: Université Lille 1, France Type: Séminaire problèmes spectraux en physique mathématique Site: IHP Salle: 314 Date de début: 24/11/2014 - 14:00 Date de fin: 24/11/2014 - 14:00

In this talk we consider a model for a nucleon interacting with the $\sigma$ and $\omega$ mesons in the atomic nucleus. The model is relativistic, but we study it in the nuclear physics nonrelativistic limit where is described by a nonlinear Schrödinger-type equation with a mass which depends on the solution itself. After discussing some previous results on the existence of positive solutions, I will prove the uniqueness and nondegeneracy of these ones. As an application, I will construct solutions to the relativistic $\sigma$ and $\omega$ model, which consists of one Dirac equation coupled to two Klein-Gordon equations.

The talk is based on joint work with Mathieu Lewin