Dynamic properties, Gaussian soliton and chaotic behaviors of general Degasperis-Procesi model

We establish the existences of periodic and soliton solutions to unperturbed general Degasperis-Procesi model, and corresponding solutions are shown to verify it. Especially, the Gaussian solitons are presented, which are barely seen in non-logarithmic equation. Moreover, the stability of soliton and modulation instability of the original equation are analyzed. Finally, by taking the external perturbed terms into consideration, the chaotic behaviors emerge. Corresponding largest Lyapunov exponents and phase portraits are presented to verify our conclusion graphically. The results such as Gaussian soliton solutions and chaotic behavior for the general Degasperis-Procesi model are initially discovered in the present paper.