Linear instability and uniqueness of the peaked periodic wave in the reduced Ostrovsky equation

Anna Geyer, Dmitry Pelinovsky

Research output: Contribution to journalArticleScientificpeer-review

7 Citations (Scopus)

Abstract

The stability of the peaked periodic wave in the reduced Ostrovsky equation has remained an open problem for a long time. In order to solve this problem we obtain sharp bounds on the exponential growth of the L 2 norm of co-periodic perturbations to the peaked periodic wave, from which it follows that the peaked periodic wave is linearly unstable. We also prove that the peaked periodic wave with a parabolic profile is the unique peaked wave in the space of periodic L 2 functions with zero mean and a single minimum per period.

Original languageEnglish
Pages (from-to)1188-1208
Number of pages21
JournalSIAM Journal on Mathematical Analysis
Volume51
Issue number2
DOIs
Publication statusPublished - 2019

Keywords

  • Characteristics
  • Instability
  • Peaked periodic wave
  • Reduced Ostrovsky equation
  • Semigroup

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