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

Tohru Ozawa, Hideaki Sunagawa

    Research output: Contribution to journalArticle

    18 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

      Fingerprint

    Keywords

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

    ASJC Scopus subject areas

    • Analysis
    • Applied Mathematics

    Cite this