Transverse instability for a system of nonlinear schrödinger equations

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Abstract

In this paper, we consider the transverse instability for a system of nonlinear Schrödinger equations on R × TL. Here, T L means the torus with a 2πL period. It was shown by Colin-Ohta [11] that this system on R has a stable standing wave. In this paper, we regard this standing wave as the standing wave of this system on R × T L. Then, we show that there exists the critical period Lσ which is the boundary between the stability and the instability of the standing wave on R × TL.

Original languageEnglish
Pages (from-to)565-588
Number of pages24
JournalDiscrete and Continuous Dynamical Systems - Series B
Volume19
Issue number2
DOIs
Publication statusPublished - Mar 2014
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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