BCAM Course | Rigorous derivation of the Wave Kinetic Equation for NLS

The aim of this course is to present recent developments in the theory of non-equilibrium statistical physics for nonlinear waves, commonly known as wave  turbulence. A large system of weakly-interacting waves is generally governed by a large number of differential equations which describe the dynamics of each wave. Due to their complexity and the large number of waves, the precise description of an individual wave may be difficult, and it might not be representative of the behavior of the system as a whole. What is sometimes possible is a statistical description of such a system, which provides information about its typical behavior. We will present such a description, in the form of a Wave Kinetic Equation, in the case where the underlying “microscopic” system of nonlinear waves satisfies the cubic Schrödinger equation, and show how to derive it rigorously.
 

More information about the program of the course: https://www.bcamath.org/events/bcamcourse-20250127-rdwkenls/en/