Spacetime quasiperiodic solutions to a nonlinear Schrödinger equation on Z-Reference-Cited by-同舟云学术

Spacetime quasiperiodic solutions to a nonlinear Schrödinger equation on Z

Published:2024-01-01 Issue:1 Volume:65 Page:
ISSN:0022-2488
Container-title:Journal of Mathematical Physics
language:en
Short-container-title:

Author:

Kachkovskiy Ilya¹^ORCID,Liu Wencai²^ORCID,Wang Wei-Min³^ORCID

Affiliation:

1. Department of Mathematics, Michigan State University 1 , Wells Hall, 619 Red Cedar Rd., East Lansing, Michigan 48824, USA

2. Department of Mathematics, Texas A&M University 2 , College Station, Texas 77843-3368, USA

3. CNRS and Département de Mathématique, Cergy Paris Université 3 , 95302 Cergy-Pontoise Cedex, France

Abstract

We consider a discrete non-linear Schrödinger equation on Z and show that, after adding a small potential localized in the time-frequency space, one can construct a three-parametric family of non-decaying spacetime quasiperiodic solutions to this equation. The proof is based on the Craig–Wayne–Bourgain method combined with recent techniques of dealing with Anderson localization for two-dimensional quasiperiodic operators with degenerate frequencies.

Funder

National Science Foundation

Alfred P. Sloan Foundation

CY Initiative of Excellence “Investissements d'Avenir;”

Publisher

AIP Publishing

Subject

Mathematical Physics,Statistical and Nonlinear Physics

Link

https://pubs.aip.org/aip/jmp/article-pdf/doi/10.1063/5.0166183/18284440/011502_1_5.0166183.pdf

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