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Stability of Periodic, Traveling-Wave Solutions to the Capillary Whitham Equation
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Stability of Periodic, Traveling-Wave Solutions to the Capillary Whitham Equation
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Journal Article
Stability of Periodic, Traveling-Wave Solutions to the Capillary Whitham Equation
2019
Overview
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.
Publisher
MDPI AG
