Wave turbulence for the nonlinear Schrödinger equation

2018/07/13 Fri 15:30 - 17:00
Room 251, Building No.3
Jalal Shatah
New York University

Wave turbulence describes the out-of-equilibrium statistical mechanics of weakly nonlinear waves. It was first put forward by Peierls in 1928, in the context of solid state physics, and then by Hasselman in 1962, in the context of water waves. The theory was invigorated and investigated by Zakharov and his school in the 70's. The theory of weak turbulence proposed by Zakharov relies on the derivation of a kinetic wave equation. In this talk we will derive the kinetic equation for the nonlinear Schrödinger equation and discuss the time scale where the kinetic equation is a valid approximation.