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

Academic Article


  • 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.
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    Author List

  • Georgiev V; Stefanov A
  • Start Page

  • 29
  • End Page

  • 39
  • Volume

  • 370