Bifurcation of traveling wave solutions of (2Â +Â 1) dimensional Konopelchenko-Dubrovsky equations

The bifurcation theory method of planar dynamical systems is efficiently employed to find the bounded traveling wave solutions of the (2 + 1) dimensional Konopelchenko-Dubrovsky equations. The bifurcation parameter sets and the corresponding phase portraits are given. Under different parameter conditions, the exact explicit parametric representations of solitary wave solutions, kink (anti-kink) wave solutions and periodic wave solutions are obtained.