Solitary wave solutions to a class of Whitham-Boussinesq systems

In this note we study solitary wave solutions of a class of Whitham-Boussinesq systems which includes the bi-directional Whitham system as a special example. The travelling wave version of the evolution system can be reduced to a single evolution equation, similar to a class of equations studied by Ehrnstr\"om, Groves and Wahl\'en. In that paper the authors prove the existence of solitary wave solutions using a constrained minimization argument adapted to noncoercive functionals, developed by Buffoni, Groves and Wahl\'en, together with the concentration-compactness principle.