Exact Peakon, Periodic Peakon and Solitary Wave Solutions of the KdV-Like Advection-Dispersion Equation

In this paper, we investigate a class of KdV-like advection-dispersion equations and derive explicit exact solutions describing various nonlinear wave phenomena, including peakon, periodic peakon, and smooth wave solutions. By using the method of dynamical systems, under given parameter conditions, we obtain bifurcations of the phase portraits for the corresponding traveling wave dynamical system. Corresponding to different level curves, we derive exact explicit parametric representations of the periodic peakon, peakon, smooth periodic wave solution as well as solitary wave solutions.