New exact traveling wave solutions for the Klein–Gordon–Zakharov equations

Based on the extended hyperbolic functions method, we obtain the multiple exact explicit solutions of the Klein–Gordon–Zakharov equations. The solutions obtained in this paper include (a) the solitary wave solutions of bell-type for u and n, (b) the solitary wave solutions of kink-type for u and bell-type for n, (c) the solitary wave solutions of a compound of the bell-type and the kink-type for u and n, (d) the singular traveling wave solutions, (e) periodic traveling wave solutions of triangle function types, and solitary wave solutions of rational function types. We not only rederive all known solutions of the Klein–Gordon–Zakharov equations in a systematic way but also obtain several entirely new and more general solutions. The variety of structures of the exact solutions of the Klein–Gordon–Zakharov equations is illustrated.