Onset of the wave turbulence description of the longtime behavior of the nonlinear Schrödinger equation-Reference-Cited by-同舟云学术

Onset of the wave turbulence description of the longtime behavior of the nonlinear Schrödinger equation

Published:2021-03-18 Issue:3 Volume:225 Page:787-855
ISSN:0020-9910
Container-title:Inventiones mathematicae
language:en
Short-container-title:Invent. math.

Author:

Buckmaster T.,Germain P.,Hani Z.,Shatah J.

Abstract

AbstractConsider the cubic nonlinear Schrödinger equation set on a d-dimensional torus, with data whose Fourier coefficients have phases which are uniformly distributed and independent. We show that, on average, the evolution of the moduli of the Fourier coefficients is governed by the so-called wave kinetic equation, predicted in wave turbulence theory, on a nontrivial timescale.

Publisher

Springer Science and Business Media LLC

Subject

General Mathematics

Link

https://link.springer.com/content/pdf/10.1007/s00222-021-01039-z.pdf

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