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Open AccessArticle

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

by *,† and
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)
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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MDPI and ACS Style

Carter, J.D.; Rozman, M. Stability of Periodic, Traveling-Wave Solutions to the Capillary Whitham Equation. Fluids 2019, 4, 58. https://doi.org/10.3390/fluids4010058

AMA Style

Carter JD, Rozman M. Stability of Periodic, Traveling-Wave Solutions to the Capillary Whitham Equation. Fluids. 2019; 4(1):58. https://doi.org/10.3390/fluids4010058

Chicago/Turabian Style

Carter, John D.; Rozman, Morgan. 2019. "Stability of Periodic, Traveling-Wave Solutions to the Capillary Whitham Equation" Fluids 4, no. 1: 58. https://doi.org/10.3390/fluids4010058

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