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Bibliographic Details
Main Authors: Carles, Remi, Faou, Erwan
Format: Preprint
Published: 2010
Subjects:
Online Access:https://arxiv.org/abs/1010.5173
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author Carles, Remi
Faou, Erwan
author_facet Carles, Remi
Faou, Erwan
contents We consider the nonlinear Schrodinger equation with cubic (focusing or defocusing) nonlinearity on the multidimensional torus. For special small initial data containing only five modes, we exhibit a countable set of time layers in which arbitrarily large modes are created. The proof relies on a reduction to multiphase weakly nonlinear geometric optics, and on the study of a particular two-dimensional discrete dynamical system.
format Preprint
id arxiv_https___arxiv_org_abs_1010_5173
institution arXiv
publishDate 2010
record_format arxiv
spellingShingle Energy cascades for NLS on the torus
Carles, Remi
Faou, Erwan
Analysis of PDEs
Mathematical Physics
Primary 35Q55, Secondary 35C20, 37K55
We consider the nonlinear Schrodinger equation with cubic (focusing or defocusing) nonlinearity on the multidimensional torus. For special small initial data containing only five modes, we exhibit a countable set of time layers in which arbitrarily large modes are created. The proof relies on a reduction to multiphase weakly nonlinear geometric optics, and on the study of a particular two-dimensional discrete dynamical system.
title Energy cascades for NLS on the torus
topic Analysis of PDEs
Mathematical Physics
Primary 35Q55, Secondary 35C20, 37K55
url https://arxiv.org/abs/1010.5173