Abstract
A modified generalized KdV equation is considered in this paper. Under the given parameter conditions, the corresponding traveling wave system is a singular planar dynamical system with three singular straight lines. The bifurcations and traveling wave solutions of the system are investigated in the parameter space from the perspective of dynamical systems. The existence of solitary wave solutions, periodic peakon solutions, pseudo-peakon solutions, kink and anti-kink wave solutions and compactons is proved. Furthermore, possible exact explicit parametric representations of various solutions are given. Particularly, the model has uncountably infinite many solitary wave and pseudo-peakon solutions.
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