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

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    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
    Issue number8
    Publication statusPublished - 2017 Aug 1



    • Schrödinger
    • Stability
    • uniqueness

    ASJC Scopus subject areas

    • Analysis
    • Discrete Mathematics and Combinatorics
    • Applied Mathematics

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