Smooth and non-smooth traveling wave solutions of a class of nonlinear dispersive equation

There is the widespread existence of wave phenomena in physics, mechanics. This clearly necessitates a study of traveling waves in depth and of the modeling and analysis involved. In this paper, we study a nonlinear dispersive K(n,−n,2n) equation, which can be regarded as a generalized K(n,n) equation. Applying the bifurcation theory and the method of phase portraits analysis, we obtain the dynamical behavior and special exact solutions of the K(n,−n,2n) equation. As a result, the conditions under which peakon and compacton solutions appear are also given and the analytic expressions of peakon solutions, compacton and periodic cusp wave solutions are obtained.