%0 Journal Article
%T Stability of Periodic, Traveling-Wave Solutions to the Capillary Whitham Equation
%A John D. Carter
%A Morgan Rozman
%J -
%D 2019
%R https://doi.org/10.3390/fluids4010058
%X 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-Tex
%K Whitham equation
%K fully-dispersive
%K surface tension
%K traveling-wave solutions
%K stability
%U https://www.mdpi.com/2311-5521/4/1/58