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

John D. Carter, Morgan Rozman
2019 Fluids  
Recently, the Whitham and capillary Whitham equations were shown to accurately modelthe evolution of surface waves on shallow water. In order to gain a deeper understanding of theseequations, we compute periodic, traveling-wave solutions for both and study their stability. Wepresent plots of a representative sampling of solutions for a range of wavelengths, wave speeds, waveheights, and surface tension values. Finally, we discuss the role these parameters play in the stabilityof these solutions.
doi:10.3390/fluids4010058 fatcat:6br6hxjl2fawxn7eezxayil36m