Spectral instability of the peaked periodic wave in the reduced ostrovsky equations

Anna Geyer, Dmitry E. Pelinovsky

Research output: Contribution to journalArticleScientificpeer-review

1 Citation (Scopus)
2 Downloads (Pure)

Abstract

We show that the peaked periodic traveling wave of the reduced Ostrovsky equations with quadratic and cubic nonlinearity is spectrally unstable in the space of square integrable periodic functions with zero mean and the same period. We discover that the spectrum of a linearized operator at the peaked periodic wave completely covers a closed vertical strip of the complex plane. In order to obtain this instability, we prove an abstract result on spectra of operators under compact perturbations. This justifies the truncation of the linearized operator at the peaked periodic wave to its differential part for which the spectrum is then computed explicitly.

Original languageEnglish
Pages (from-to)5109-5125
Number of pages17
JournalProceedings of the American Mathematical Society
Volume148
Issue number12
DOIs
Publication statusPublished - 2020

Keywords

  • Peaked periodic wave
  • Reduced Ostrovsky equation
  • Spectral instability

Fingerprint Dive into the research topics of 'Spectral instability of the peaked periodic wave in the reduced ostrovsky equations'. Together they form a unique fingerprint.

Cite this