Bifurcation of traveling wave solutions of a generalized K(n, n) equation

In this article, a generalized K(n, n) equation is studied by the qualitative theory of bifurcations and the method of dynamical systems. The result shows the existence of the different kinds of traveling solutions of the generalized K(n, n) equation, including solitary waves, kink waves, periodic wave and compacton solutions, which depend on different parametric ranges. Moreover, various sufficient conditions to guarantee the existence of the above traveling solutions are provided under different parameters conditions.