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