Analyticity of solutions to the non gauge invariant Schrödinger equations

Gaku Hoshino, Pavel I. Naumkin

    Research output: Contribution to journalArticle

    1 Citation (Scopus)

    Abstract

    We study the global Cauchy problem for the non gauge invariant Schrödinger equations (Formula Presented). The application of the Galilei generator for the proof of the analytic smoothing effect of solutions to the Cauchy problem for non gauge invariant Schrödinger equations involves diffculties. In this paper we construct analytic solutions to the non gauge invariant Schrödinger equations in the case of analytic and suffciently small initial data. We use the power like analytic spaces and the analytic Hardy spaces as auxiliary analytic spaces characterized by the Galilei generator. Also we show that if the initial data ϕ decay exponentially and are suffciently small in an appropriate norm, then the solutions of the Cauchy problem for non gauge invariant Schrödinger equations exist globally in time and are analytic.

    Original languageEnglish
    Pages (from-to)65-75
    Number of pages11
    JournalFunkcialaj Ekvacioj
    Volume60
    Issue number1
    DOIs
    Publication statusPublished - 2017

    Keywords

    • Analytic smoothing effect
    • Analytic solutions
    • Nonlinear Schrödinger equation

    ASJC Scopus subject areas

    • Analysis
    • Algebra and Number Theory
    • Geometry and Topology

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