Workshop: Soliton gas for the focusing nonlinear Schrödinger equation

Speaker
Grava, University of Bristol

Abstract
We consider a gas of random N solitons for the focusing nonlinear Schrödinger equation and we study the limit as N goes to infinity. The N points of the discrete spectrum of the Zakharov-Shabat  linear operator corresponding to the N soliton solution are random variables sampled from various probability distributions while the norming constants are interpolated  by a smooth function evaluated at the spectral point. We derive the limiting solution  and we prove that, for fixed values of position and time, the fluctuation of the $N$-soliton solution, around its limiting value, is a Gaussian random variable.