Transverse instability for nonlinear Schrödinger equation with a linear potential

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Abstract

In this paper, we consider the transverse instability for a nonlinear Schrödinger equation with a linear potential on R×TL, where 2πL is the period of the torus TL. Rose and Weinstein [18] showed the existence of a stable standing wave for a nonlinear Schrödinger equation with a linear potential. We regard the standing wave of nonlinear Schrödinger equation on R as a line standing wave of nonlinear Schrödinger equation on R×TL. We show the stability of line standing waves for all L > 0 by using the argument of the previous paper [26].

Original languageEnglish
Pages (from-to)429-462
Number of pages34
JournalAdvances in Differential Equations
Volume21
Issue number5-6
Publication statusPublished - 2016
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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