Analytic smoothing effect for the cubic hyperbolic schrödinger equation in two space dimensions

Gaku Hoshino, Tohru Ozawa

    Research output: Contribution to journalArticle

    2 Citations (Scopus)

    Abstract

    We study the Cauchy problem for the cubic hyperbolic Schrödinger equation in two space dimensions. We prove existence of analytic global solutions for sufficiently small and exponential decaying data. The method of proof depends on the generalized Leibniz rule for the generator of pseudo-conformal transform acting on pseudo-conformally invariant nonlinearity.

    Original languageEnglish
    JournalElectronic Journal of Differential Equations
    Volume2016
    Publication statusPublished - 2016 Jan 25

    Fingerprint

    Leibniz' rule
    Smoothing Effect
    Cubic equation
    Hyperbolic Equations
    Global Solution
    Cauchy Problem
    Nonlinearity
    Generator
    Transform
    Invariant

    Keywords

    • Analytic smoothing effect
    • Global solution
    • Non elliptic Schrödinger equation
    • Nonlinear Schrödinger equation

    ASJC Scopus subject areas

    • Analysis

    Cite this

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    title = "Analytic smoothing effect for the cubic hyperbolic schr{\"o}dinger equation in two space dimensions",
    abstract = "We study the Cauchy problem for the cubic hyperbolic Schr{\"o}dinger equation in two space dimensions. We prove existence of analytic global solutions for sufficiently small and exponential decaying data. The method of proof depends on the generalized Leibniz rule for the generator of pseudo-conformal transform acting on pseudo-conformally invariant nonlinearity.",
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    publisher = "Texas State University - San Marcos",

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    AU - Ozawa, Tohru

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    N2 - We study the Cauchy problem for the cubic hyperbolic Schrödinger equation in two space dimensions. We prove existence of analytic global solutions for sufficiently small and exponential decaying data. The method of proof depends on the generalized Leibniz rule for the generator of pseudo-conformal transform acting on pseudo-conformally invariant nonlinearity.

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    KW - Global solution

    KW - Non elliptic Schrödinger equation

    KW - Nonlinear Schrödinger equation

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    JO - Electronic Journal of Differential Equations

    JF - Electronic Journal of Differential Equations

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