Michela PROCESI - 1/3 Recurrent and diffusive dynamics for the NLS equation on tori
Channel: Institut des Hautes Études Scientifiques (IHÉS)
Date: 2016-07-27

Small  solutions  of  the  NLS  equation  on  tori  may  exhibit  very  different qualitative behavior. In order to illustrate this phenomenon, I will discuss various classes   of special solutions for the NLS on the circle and on the two   dimensional torus. On the one hand I shall prove existence of stable and unstable  quasi-periodic solutions, on the other hand I shall study solutions   which transfer energy to high Fourier modes. This analysis relies on the rich combinatorial structure of the Birkhoff Hamiltonian of the NLS.