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

Vladimir Georgiev, Atanas Stefanov*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


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
Publication statusPublished - 2018 May 1


  • Ground states
  • Hartree equation
  • Semilinear

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics


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