Finite charge solutions to cubic schrödinger equations with a nonlocal nonlinearity in one space dimension

Kei Nakamura, Tohru Ozawa

    Research output: Contribution to journalArticle

    1 Citation (Scopus)

    Abstract

    We study the Cauchy problem for cubic Schrödinger equations modelling ultra-short laser pulses propagating along the line. The global existence, blow-up, and scattering of solutions is described exclusively in the charge space L 2(R) without any approximating arguments.

    Original languageEnglish
    Pages (from-to)789-801
    Number of pages13
    JournalDiscrete and Continuous Dynamical Systems- Series A
    Volume33
    Issue number2
    DOIs
    Publication statusPublished - 2013

    Fingerprint

    Ultrashort Laser Pulses
    Cubic equation
    L-space
    Ultrashort pulses
    Electric space charge
    Global Existence
    Blow-up
    Cauchy Problem
    Charge
    Scattering
    Nonlinearity
    Line
    Modeling

    Keywords

    • Blow-up
    • Nonlinear Schrödinger equations
    • Scattering.

    ASJC Scopus subject areas

    • Discrete Mathematics and Combinatorics
    • Applied Mathematics
    • Analysis

    Cite this

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    title = "Finite charge solutions to cubic schr{\"o}dinger equations with a nonlocal nonlinearity in one space dimension",
    abstract = "We study the Cauchy problem for cubic Schr{\"o}dinger equations modelling ultra-short laser pulses propagating along the line. The global existence, blow-up, and scattering of solutions is described exclusively in the charge space L 2(R) without any approximating arguments.",
    keywords = "Blow-up, Nonlinear Schr{\"o}dinger equations, Scattering.",
    author = "Kei Nakamura and Tohru Ozawa",
    year = "2013",
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    language = "English",
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    pages = "789--801",
    journal = "Discrete and Continuous Dynamical Systems- Series A",
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    publisher = "Southwest Missouri State University",
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    AU - Nakamura, Kei

    AU - Ozawa, Tohru

    PY - 2013

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    KW - Nonlinear Schrödinger equations

    KW - Scattering.

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    JO - Discrete and Continuous Dynamical Systems- Series A

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