Mathematics Seminar Series: Harmonic Analysis and Differential Equations (HADES)

Title: From waves to particles, a journey for bound states in NLS.

Abstract: While the title seems to be more fiction than science, I will present rigorous results. Namely, in a certain extreme regime, bound states for Schrödinger equation with attractive power nonlinearity behave like a collection of particles. The interaction laws between these particles can be explicitly determined, hence we can infer the existence of equilibria i.e., bound states in this extreme regime, and their properties. Moreover, I will also show that the extreme regime and its bound states have very important implications on the behavior of solutions in the “normal” regime.