Long time stability of small finite gap solutions of the cubic Nonlinear Schrödinger equation on the two dimensional torus

Talk by Dr. Alberto Maspero

Speaker invited by: Prof. Dr. Thomas Kappeler

Date: 31.05.18  Time: 18.10 - 19.00  Room: Y27H35/36

Abstract: We study long time stability of a class of nontrivial, quasi-periodic solutions depending on one spacial variable of the cubic defocusing non-linear Schrödinger equation on the two dimensional torus. We prove that these quasi-periodic solutions are orbitally stable for finite but long times, provided that their Fourier support and their frequency vector satisfy some complicated but explicit condition, which we show holds true for most solutions. This is a joint work with M. Procesi.