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
