Solitary wave solutions of a generalization of the mKdV equation

TL;DR

This paper explores solitary wave solutions, including classical, peakons, and cuspons, for a generalized mKdV equation with dissipation terms akin to those in well-known integrable and non-integrable equations.

Contribution

It introduces a generalized mKdV equation with dissipation and constructs various types of solitary wave solutions, expanding understanding of wave phenomena in dissipative systems.

Findings

Existence of classical solitons in the generalized equation

Construction of peakon solutions with peaked profiles

Identification of cuspon solutions with cusped structures

Abstract

We consider a generalization of the mKdV equation, which contains dissipation terms similar to those contained in both the Benjamin-Bona-Mahoney equation and the famous Camassa-Holm and Degasperis-Procesi equations. Our objective is the construction of classical (solitons) and non-classical (peakons and cuspons) solitary wave solutions of this equation.