Abstract for the talk on 21.07.2016 (11:00 h)Arbeitsgemeinschaft ANGEWANDTE ANALYSIS
Simona Rota-Nodari (MPI MIS, Leipzig)
On a nonlinear Schrödinger equation for nucleons
In this talk we consider a model for a nucleon interacting with the σ and ω 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 non-degeneracy of these ones. As an application, I will construct solutions to the relativistic σ and ω model, which consists of one Dirac equation coupled to two Klein-Gordon equations. The talk is based on joint works with M.J. Esteban, L. Le Treust and Mathieu Lewin.