Prof. Tamara Grava | Plenary talk: Soliton gas for the focusing nonlinear Schrödinger equation

Speaker: Professor Tamara Grava (SISSA)
Date: 30th Jul 2024
Title: Plenary talk: Soliton gas for the focusing nonlinear Schrödinger equation
Event: (PDWW01) Frontiers of Dispersive Hydrodynamics
Abstract: We consider a gas of random N solitons for the focusing nonlinear Schr ̈odinger equation and we study the limit as N goes to infinity. The randomness is chosen as follow: the N points of the discrete spectrum of the Zakharov-Shabat linear operator corresponding to the N soliton solution are independent identically distributed random variables sampled from a probability measure of a compact domain of the complex plane, while the norming constants are interpolated by a smooth function evaluated at the spectral point. We derive the limiting solution [2] and we prove that, for fixed values of position and time, the fluctuation of the N-soliton solution around its limiting value is Gaussian random variable [1].[1] M. Bertola, T. Grava, G. Orsatti, Soliton shielding of the focusing nonlinear Schr ̈odinger equation Phys. Rev. Lett. 130, (2023), no. 12, Paper No. 127201, 6 pp. and work in progress.[2] Work in progress with M. Girotti, T.Grava, K. McLaughlin and J. Najnudel.
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