Soliton dynamics for the general Degasperis-Procesi equation

TL;DR

This paper investigates soliton solutions within a broad family of shallow water equations, providing criteria for their existence and exploring their interactions in nonintegrable cases.

Contribution

It introduces a new criterion for the existence of smooth soliton solutions in the general Degasperis-Procesi model, encompassing several well-known equations.

Findings

Criteria for smooth soliton existence

Analysis of soliton interactions in nonintegrable cases

Unification of multiple shallow water models

Abstract

We consider the general Degasperis-Procesi model of shallow water out-flows. This fife parametric family of conservation laws contains, in particular, KdV, Camassa-Holm, and Degasperis-Procesi equations. The main result consists of a criterion which guarantees the existence of a smooth soliton type solution. We discuss also the scenario of soliton interaction for this model in the nonintegrable case.