On the classification of the spectrally stable standing waves of the Hartree problem

    Research output: Contribution to journalArticle

    1 Citation (Scopus)

    Abstract

    We consider the fractional Hartree model, with general power non-linearity and arbitrary spatial dimension. We construct variationally the “normalized” solutions for the corresponding Choquard–Pekar model—in particular a number of key properties, like smoothness and bell-shapedness are established. As a consequence of the construction, we show that these solitons are spectrally stable as solutions to the time-dependent Hartree model. In addition, we analyze the spectral stability of the Moroz–Van Schaftingen solitons of the classical Hartree problem, in any dimensions and power non-linearity. A full classification is obtained, the main conclusion of which is that only and exactly the “normalized” solutions (which exist only in a portion of the range) are spectrally stable.

    Original languageEnglish
    Pages (from-to)29-39
    Number of pages11
    JournalPhysica D: Nonlinear Phenomena
    Volume370
    DOIs
    Publication statusPublished - 2018 May 1

    Keywords

    • Ground states
    • Hartree equation
    • Semilinear

    ASJC Scopus subject areas

    • Statistical and Nonlinear Physics
    • Condensed Matter Physics

    Fingerprint Dive into the research topics of 'On the classification of the spectrally stable standing waves of the Hartree problem'. Together they form a unique fingerprint.

  • Cite this