High frequency solutions for the singularly-perturbed one-dimensional nonlinear Schrödinger equation

Patricio Felmer, Salomé Martínez, Kazunaga Tanaka

    Research output: Contribution to journalArticle

    9 Citations (Scopus)

    Abstract

    This article is devoted to the nonlinear Schrödinger equation [InlineMediaObject not available: see fulltext.] when the parameter ε approaches zero. All possible asymptotic behaviors of bounded solutions can be described by means of envelopes, or alternatively by adiabatic profiles. We prove that for every envelope, there exists a family of solutions reaching that asymptotic behavior, in the case of bounded intervals. We use a combination of the Nehari finite dimensional reduction together with degree theory. Our main contribution is to compute the degree of each cluster, which is a key piece of information in order to glue them.

    Original languageEnglish
    Pages (from-to)333-366
    Number of pages34
    JournalArchive for Rational Mechanics and Analysis
    Volume182
    Issue number2
    DOIs
    Publication statusPublished - 2006 Oct

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    Glues
    Singularly Perturbed
    Nonlinear equations
    Envelope
    Nonlinear Equations
    Finite-dimensional Reduction
    Asymptotic Behavior
    Degree Theory
    Bounded Solutions
    Interval
    Zero
    Profile
    Family

    ASJC Scopus subject areas

    • Mechanics of Materials
    • Computational Mechanics
    • Mathematics(all)
    • Mathematics (miscellaneous)

    Cite this

    High frequency solutions for the singularly-perturbed one-dimensional nonlinear Schrödinger equation. / Felmer, Patricio; Martínez, Salomé; Tanaka, Kazunaga.

    In: Archive for Rational Mechanics and Analysis, Vol. 182, No. 2, 10.2006, p. 333-366.

    Research output: Contribution to journalArticle

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