Graduate Student / Postdoc Seminar

Resonances, quasi-resonances, and Wave Turbulence

Speaker: Jalal Shatah, Courant Institute of Mathematical Sciences

Location: Warren Weaver Hall 1302

Date: Friday, October 26, 2018, 1 p.m.


Resonances and quasi-resonances play a major role in the long time dynamics of nonlinear waves. In this talk we will explain their impact starting with ODEs and ending with nonlinear dispersive equations, where resonances lead to kinetic equations and wave turbulence. We will explain the different types of mathematics involved in deriving  the kinetic equation for the nonlinear Schr\"odinger equation and the time scale where the kinetic equation is a valid approximation for the long time dynamics.