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arXiv · 2101.06601

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

Ryan Creedon·Bernard Deconinck·Olga Trichtchenko
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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.

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Ryan Creedon, Bernard Deconinck, Olga Trichtchenko. 2021-01-17. High-Frequency Instabilities of the Kawahara Equation: A Perturbative Approach. https://arxiv.org/abs/2101.06601

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