Spectral Stability for Classical Periodic Waves of the Ostrovsky and Short Pulse Models

HAKKAEV S. A., Stanislavova M., Stefanov A.

Studies in Applied Mathematics, vol.139, no.3, pp.405-433, 2017 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 139 Issue: 3
  • Publication Date: 2017
  • Doi Number: 10.1111/sapm.12166
  • Journal Name: Studies in Applied Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.405-433
  • Trakya University Affiliated: No

Abstract

We consider the Ostrovsky and short pulse models in a symmetric spatial interval, subject to periodic boundary conditions. For the Ostrovsky case, we rederive the formulas for the classical periodic traveling waves, while for the short pulse model, we explicitly construct traveling waves in terms of Jacobi elliptic functions. In both cases, we show spectral stability, for all values of the parameters. This is achieved by studying the nonstandard eigenvalue problems in the form L[u]=λu’, where L is a Hill operator.