Abstract
In this paper, we consider a Camassa and Holm-Degasperis and Procesi
(CH-DP) equation $u_{t}-
c_{0}u_{x}+4uu_{x}-\alpha^2(u_{xxt}+uu_{xxx}+3u_{x}u_{xx})+\gamma
u_{xxx}=0$. By using the bifurcation method of dynamical systems,
some new explicit compacton and generalized kink wave solutions are
presented through some special phase orbits. The results of before
references are extended.