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

Vladimir Georgiev, Atanas Stefanov

Research output: Contribution to journalArticlepeer-review

Abstract

We consider the fractional Hartree model, with general power non-linearity and space 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.

MSC Codes 35Q55, 35P10, 42B37, 42B35

Original languageEnglish
JournalUnknown Journal
Publication statusPublished - 2017 Feb 10

Keywords

  • Ground states
  • Klein-Gordon equation
  • Schrödinger equation
  • Semilinear

ASJC Scopus subject areas

  • General

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