Bifurcation of travelling wave solutions in generalized phi-four equation

By using the method of planar dynamical systems to a nonlinear variant of the phi-four equation, the existence of smooth and nonsmooth solitary wave (so called peakon and valleyon) and infinite many periodic wave solutions is shown. Under different regions of parametric spaces, various sufficient conditions to guarantee the existence of above solutions are given. The formulas to compute the travelling waves are also educed.