Travelling waves in a dispersion-saturating diffusion equation

TL;DR

This paper investigates monotone travelling wave solutions in a generalized Rosenau-Korteweg de Vries equation, establishing their existence and stability properties within a framework that combines diffusion and dispersion effects.

Contribution

It provides new existence and stability results for travelling waves in a dispersion-saturating diffusion equation, extending understanding of wave behavior in such models.

Findings

Existence of monotone travelling waves proved.

Linear and nonlinear stability results established.

Analysis covers various regimes of the equation.

Abstract

In the framework of hyperbolic conservation laws regularised by including diffusive and dispersive terms, we study monotone travelling waves for the generalised Rosenau-Korteweg de Vries equation. We establish existence as well as linear and nonlinear determinacy results in different regimes.