Bifurcations and Exact Solutions of the Coupled Nonlinear Generalized Zakharov Equations with Anti-Cubic Nonlinearity: Dynamical System Approach

We consider the exact traveling wave solutions for the coupled nonlinear generalized Zakharov equations. By employing the method of dynamical systems, we are able to obtain bifurcations of the phase portraits of the corresponding planar dynamical system under various parameter conditions. Based on different level curves, we derive all possible exact explicit parametric representations of bounded solutions, which include pseudo-periodic peakon, pseudo-peakon, smooth periodic wave solutions, solitary solutions, kink wave solution and the compacton solution family.