Small data blow-up for a system of nonlinear Schrödinger equations

Tohru Ozawa, Hideaki Sunagawa

Research output: Contribution to journalArticle

20 Citations (Scopus)

Abstract

We give examples of small data blow-up for a three-component system of quadratic nonlinear Schrödinger equations in one space dimension. Our construction of the blowing-up solution is based on the Hopf-Cole transformation, which allows us to reduce the problem to getting suitable growth estimates for a solution to the transformed system. Amplification in the reduced system is shown to have a close connection with the mass resonance.

Original languageEnglish
Pages (from-to)147-155
Number of pages9
JournalJournal of Mathematical Analysis and Applications
Volume399
Issue number1
DOIs
Publication statusPublished - 2013 Mar 1

Keywords

  • Hopf-Cole transformation
  • Mass resonance
  • Nonlinear Schrödinger equation
  • Small data blow-up

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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