Nonlinear instability of linearly unstable standing waves for nonlinear Schrödinger equations

Vladimir Georgiev, Masahito Ohta

Research output: Contribution to journalArticle

16 Citations (Scopus)

Abstract

We study the instability of standing waves for nonlinear Schrödinger equations. Under a general assumption on nonlinearity, we prove that linear instability implies orbital instability in any dimension. For that purpose, we establish a Strichartz type estimate for the propagator generated by the linearized operator around standing wave.

Original languageEnglish
Pages (from-to)533-548
Number of pages16
JournalJournal of the Mathematical Society of Japan
Volume64
Issue number2
DOIs
Publication statusPublished - 2012 Oct 5
Externally publishedYes

Keywords

  • Instability
  • Nonlinear Schrödinger equation
  • Standing wave
  • Strichartz estimate

ASJC Scopus subject areas

  • Mathematics(all)

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