English

High-Frequency Instabilities of the Kawahara Equation: A Perturbative Approach

Analysis of PDEs 2021-01-19 v1 Dynamical Systems

Abstract

We analyze the spectral stability of small-amplitude, periodic, traveling-wave solutions of the Kawahara equation. These solutions exhibit high-frequency instabilities when subject to bounded perturbations on the whole real line. We introduce a formal perturbation method to determine the asymptotic growth rates of these instabilities, among other properties. Explicit numerical computations are used to verify our asymptotic results.

Keywords

Cite

@article{arxiv.2101.06601,
  title  = {High-Frequency Instabilities of the Kawahara Equation: A Perturbative Approach},
  author = {Ryan Creedon and Bernard Deconinck and Olga Trichtchenko},
  journal= {arXiv preprint arXiv:2101.06601},
  year   = {2021}
}

Comments

20 pages, 7 figures