Orbital stability and uniqueness of the ground state for the non-linear schrödinger equation in dimension one

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    1 Citation (Scopus)

    Abstract

    We prove that standing-waves which are solutions to the non-linear Schrödinger equation in dimension one, and whose profiles can be obtained as minima of the energy over the mass, are orbitally stable and non-degenerate, provided the non-linear term satisfies a Euler differential inequality. When the non-linear term is a combined pure power-type, then there is only one positive, symmetric minimum of prescribed mass.

    Original languageEnglish
    Pages (from-to)4309-4328
    Number of pages20
    JournalDiscrete and Continuous Dynamical Systems- Series A
    Volume37
    Issue number8
    DOIs
    Publication statusPublished - 2017 Aug 1

    Fingerprint

    Orbital Stability
    Nonlinear equations
    Ground state
    One Dimension
    Ground State
    Nonlinear Equations
    Uniqueness
    Standing Wave
    Differential Inequalities
    Term
    Euler
    Energy
    Profile

    Keywords

    • Schrödinger
    • Stability
    • uniqueness

    ASJC Scopus subject areas

    • Analysis
    • Discrete Mathematics and Combinatorics
    • Applied Mathematics

    Cite this

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    title = "Orbital stability and uniqueness of the ground state for the non-linear schr{\"o}dinger equation in dimension one",
    abstract = "We prove that standing-waves which are solutions to the non-linear Schr{\"o}dinger equation in dimension one, and whose profiles can be obtained as minima of the energy over the mass, are orbitally stable and non-degenerate, provided the non-linear term satisfies a Euler differential inequality. When the non-linear term is a combined pure power-type, then there is only one positive, symmetric minimum of prescribed mass.",
    keywords = "Schr{\"o}dinger, Stability, uniqueness",
    author = "Daniele Garrisi and Gueorguiev, {Vladimir Simeonov}",
    year = "2017",
    month = "8",
    day = "1",
    doi = "10.3934/dcds.2017184",
    language = "English",
    volume = "37",
    pages = "4309--4328",
    journal = "Discrete and Continuous Dynamical Systems- Series A",
    issn = "1078-0947",
    publisher = "Southwest Missouri State University",
    number = "8",

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    T1 - Orbital stability and uniqueness of the ground state for the non-linear schrödinger equation in dimension one

    AU - Garrisi, Daniele

    AU - Gueorguiev, Vladimir Simeonov

    PY - 2017/8/1

    Y1 - 2017/8/1

    N2 - We prove that standing-waves which are solutions to the non-linear Schrödinger equation in dimension one, and whose profiles can be obtained as minima of the energy over the mass, are orbitally stable and non-degenerate, provided the non-linear term satisfies a Euler differential inequality. When the non-linear term is a combined pure power-type, then there is only one positive, symmetric minimum of prescribed mass.

    AB - We prove that standing-waves which are solutions to the non-linear Schrödinger equation in dimension one, and whose profiles can be obtained as minima of the energy over the mass, are orbitally stable and non-degenerate, provided the non-linear term satisfies a Euler differential inequality. When the non-linear term is a combined pure power-type, then there is only one positive, symmetric minimum of prescribed mass.

    KW - Schrödinger

    KW - Stability

    KW - uniqueness

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    JF - Discrete and Continuous Dynamical Systems- Series A

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