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

Vladimir Georgiev, Atanas Stefanov*

*この研究の対応する著者

研究成果: Article査読

9 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)29-39
ページ数11
ジャーナルPhysica D: Nonlinear Phenomena
370
DOI
出版ステータスPublished - 2018 5月 1

ASJC Scopus subject areas

  • 統計物理学および非線形物理学
  • 数理物理学
  • 凝縮系物理学
  • 応用数学

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