On peaked solitary waves of Degasperis - Procesi equation

TL;DR

This paper demonstrates that the Degasperis-Procesi equation admits peaked solitary waves even when the physical parameter omega is non-zero, expanding the understanding of such waves beyond the previously known case of omega equals zero.

Contribution

It is the first to show the existence of peaked solitary waves of the DP equation for non-zero omega, broadening the scope of known wave solutions.

Findings

Peaked solitary waves exist for omega ≠ 0 in the DP equation.

The results extend the known solutions beyond the omega = 0 case.

Enhances understanding of wave phenomena in shallow water models.

Abstract

The Degasperis - Procesi (DP) equation describing the propagation of shallow water waves contains a physical parameter $\omega$, and it is well-known that the DP equation admits solitary waves with a peaked crest when $\omega = 0$. In this article, we illustrate, for the first time, that the DP equation admits peaked solitary waves even when $\omega \neq 0$. This is helpful to enrich our knowledge and deepen our understandings about peaked solitary waves of the DP equation.