Traveling-Wave Solutions of Two BiDirectional Whitham Equations

Following the work of Carter \& Rozman (2019), we study traveling wave solutions of two versions of the bidirectional Whitham equation. These equations are extensions of Boussinesq-type models that enable the phase velocities to match those of the Euler equations. We study the systems introduced by Hur \& Pandey (HP) (2018) and Aceves-S´anchez et al (2013). We compute families of periodic traveling wave solutions to the HP equation. Our goal is to compare the traveling-wave solutions of both equations to gain further understanding of the differences between them.