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Stability of Periodic, Traveling-Wave Solutions to the Capillary Whitham Equation

Mathematics Department, Seattle University, Seattle, WA 98122, USA
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Fluids 2019, 4(1), 58; https://doi.org/10.3390/fluids4010058
Received: 31 January 2019 / Revised: 12 March 2019 / Accepted: 20 March 2019 / Published: 25 March 2019
(This article belongs to the Special Issue Nonlinear Wave Hydrodynamics)
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Abstract

Recently, the Whitham and capillary Whitham equations were shown to accurately model the evolution of surface waves on shallow water. In order to gain a deeper understanding of these equations, we compute periodic, traveling-wave solutions for both and study their stability. We present plots of a representative sampling of solutions for a range of wavelengths, wave speeds, wave heights, and surface tension values. Finally, we discuss the role these parameters play in the stability of these solutions. View Full-Text
Keywords: Whitham equation; fully-dispersive; surface tension; traveling-wave solutions; stability Whitham equation; fully-dispersive; surface tension; traveling-wave solutions; stability
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Carter, J.D.; Rozman, M. Stability of Periodic, Traveling-Wave Solutions to the Capillary Whitham Equation. Fluids 2019, 4, 58.

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