High-Frequency Instabilities of the Kawahara Equation: A Perturbative Approach
arXiv:2101.06601
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.
20 pages, 7 figures