On peaked solitary waves of Degasperis - Procesi equation

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.