Prof. Jalal Shatah, gave a lecture titled “Wave turbulence for the Nonlinear Schr？dinger equation” at AMSS on 6, July 2018.
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 they derived the kinetic equation for the nonlinear Schr？dinger equation and discussed the time scale where the kinetic equationwas a valid approximation.
Prof. Jalal Shatah is from Courant Institute of New York University.