In this talk, we will study of the influence of the underlying space geometry on the asymptotic dynamics of the nonlinear Schrödinger (NLS) equation. We will consider the focusing NLS equation in the exterior of a smooth, compact, and convex obstacle with Dirichlet boundary conditions. We will study the asymptotic behavior of the solution for large times and finite time. We prove the existence of these 3 types of solutions: S
https://indico.math.cnrs.fr/event/7619/