Instability of bound states of nonlinear Schrödinger equations with Morse index equal to two

Masaya Maeda

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)

Abstract

We prove that every bound state of the nonlinear Schrödinger equation (NLS) with Morse index equal to two, with frac(d2, d ω2) (E (φ{symbol}ω) + ω Q (φ{symbol}ω)) > 0, is orbitally unstable. We apply this result to two particular cases. One is the NLS equation with potential and the other is a system of three coupled NLS equations. In both the cases the linear instability is well known but the orbital instability results are new when the spatial dimension is high.

Original languageEnglish
Pages (from-to)2100-2113
Number of pages14
JournalNonlinear Analysis, Theory, Methods and Applications
Volume72
Issue number3-4
DOIs
Publication statusPublished - 2010 Feb 1

Keywords

  • Bound states
  • Nonlinear Schrödinger equation
  • Orbital stability

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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