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arXiv · 1901.11445

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

John D. Carter·Morgan Rozman
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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 to 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 the solutions.

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John D. Carter, Morgan Rozman. 2019-01-31. Stability of Periodic, Traveling-Wave Solutions to the Capillary-Whitham Equation. https://arxiv.org/abs/1901.11445

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