Bifurcations and Exact Traveling Wave Solutions of Degenerate Coupled Multi-KdV Equations

In this paper, we consider the degenerate coupled multi-KdV equations. Depending on the coupled multiplicity l, the study of the traveling wave solutions for this model derives a series of planar dynamical systems. We consider the cases of l = 2, 3, 4. On the basis of the investigation on the dynamical behavior and bifurcations of solutions of the planar dynamical systems, we obtain all possible explicit exact parametric representations of solutions (including solitary wave solutions, periodic wave solutions, kink and anti-kink wave solutions) under different parameter conditions.