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

Kei Nakamura, Tohru Ozawa

    Research output: Contribution to journal › Article

    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

    Finite charge solutions to cubic schrödinger equations with a nonlocal nonlinearity in one space dimension. / Nakamura, Kei; Ozawa, Tohru.

    In: Discrete and Continuous Dynamical Systems- Series A, Vol. 33, No. 2, 2013, p. 789-801.

    Research output: Contribution to journal › Article

    Nakamura, K & Ozawa, T 2013, 'Finite charge solutions to cubic schrödinger equations with a nonlocal nonlinearity in one space dimension', Discrete and Continuous Dynamical Systems- Series A, vol. 33, no. 2, pp. 789-801. https://doi.org/10.3934/dcds.2013.33.789
    Nakamura K, Ozawa T. Finite charge solutions to cubic schrödinger equations with a nonlocal nonlinearity in one space dimension. Discrete and Continuous Dynamical Systems- Series A. 2013;33(2):789-801. https://doi.org/10.3934/dcds.2013.33.789
    Nakamura, Kei ; Ozawa, Tohru. / Finite charge solutions to cubic schrödinger equations with a nonlocal nonlinearity in one space dimension. In: Discrete and Continuous Dynamical Systems- Series A. 2013 ; Vol. 33, No. 2. pp. 789-801.
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    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.",
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