期刊
PHYSICS LETTERS A
卷 378, 期 30-31, 页码 2100-2107出版社
ELSEVIER SCIENCE BV
DOI: 10.1016/j.physleta.2014.04.067
关键词
Whitham; KdV; Modulational instability; Fourier-Floquet-Hill method; Dispersion; Water waves
资金
- National Science Foundation [1107476]
- Research Council of Norway [213474/F20]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1107476] Funding Source: National Science Foundation
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1107379, 1107354] Funding Source: National Science Foundation
The Whitham equation was proposed as an alternate model equation for the simplified description of unidirectional wave motion at the surface of an inviscid fluid. An advantage of the Whitham equation over the KdV equation is that it provides a more faithful description of short waves of small amplitude. Recently, Ehmstrom and Kalisch [19] established that the Whitham equation admits periodic traveling-wave solutions. The focus of this work is the stability of these solutions. The numerical results presented here suggest that all large-amplitude solutions are unstable, while small-amplitude solutions with large enough wavelength L are stable. Additionally, periodic solutions with wavelength smaller than a certain cut-off period always exhibit modulational instability. The cut-off wavelength is characterized by kh(0) = 1.145, where k = 27 pi/L is the wave number and h(0) is the mean fluid depth. (C) 2014 Elsevier B.V. All rights reserved.
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