Spectral stability of periodic waves in the generalized reduced Ostrovsky equation

Anna Geyer, Dmitry Pelinovsky

Research output: Contribution to journalArticleScientificpeer-review

7 Citations (Scopus)
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Abstract

We consider stability of periodic travelling waves in the generalized reduced Ostrovsky equation with respect to co-periodic perturbations. Compared to the recent literature, we give a simple argument that proves spectral stability of all smooth periodic travelling waves independent of the nonlinearity power. The argument is based on the energy convexity and does not use coordinate transformations of the reduced Ostrovsky equations to the semi-linear equations of the Klein–Gordon type.

Original languageEnglish
Pages (from-to)1293-1314
Number of pages22
JournalLetters in Mathematical Physics
Volume107
Issue number7
DOIs
Publication statusPublished - 2 Feb 2017

Keywords

  • Energy-to-period map
  • Negative index theory
  • Reduced Ostrovsky equations
  • Stability of periodic waves

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