Solitary wave solutions to a class of Whitham-Boussinesq systems

TL;DR

This paper investigates solitary wave solutions in a class of Whitham-Boussinesq systems, including the bi-directional Whitham system, using advanced variational methods to establish existence results.

Contribution

It extends the analysis of solitary waves to a broader class of Whitham-Boussinesq systems and applies a novel constrained minimization approach for noncoercive functionals.

Findings

Existence of solitary wave solutions in the studied systems.

Application of constrained minimization and concentration-compactness methods.

Generalization of previous results to a wider class of equations.

Abstract

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.