TRAVELING WAVES AND THEIR EVOLUTION FOR THE ZK(N,2N,-N) EQUATION

In this paper, using the approach of dynamical systems we investigate the traveling waves for the ZK(n,2n,-n) equation including the types and evolution of traveling waves. The traveling wave problem is converted into the analysis of phase portraits of the corresponding traveling wave system, which is 5-parametric and has a singular line in its phase space. The orbits passing through this singular line in phase portraits are determined by a time rescaling. After converting the orbits in these phase portraits into traveling waves, we state all types of traveling waves and give at least one exact traveling wave solution for each type of bounded traveling waves in our main results. Finally, we discuss the evolution of these traveling waves among themselves when parameters vary by the bifurcations happening in the phase portraits of the traveling wave system.