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

被引：8
|
作者：
Creedon, Ryan [1 ]
Deconinck, Bernard [1 ]
Trichtchenko, Olga [2 ]
机构：
[1] Univ Washington, Dept Appl Math, Seattle, WA 98195 USA
[2] Univ Western Ontario, Dept Phys & Astron, London, ON N6A 3K7, Canada
来源：
SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS | 2021年 / 20卷 / 03期
关键词：
Kawahara equation; spectral stability; high-frequency instabilities; perturbation methods; dispersive Hamiltonian systems; Stokes waves; PERIODIC TRAVELING-WAVES; SPECTRAL STABILITY; WATER; TRAINS; DISPERSION;
D O I：
10.1137/21M1393376
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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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页码：1571 / 1595
页数：25
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