Soliton solutions of the Klein–Gordon–Zakharov equations with power law nonlinearity

Abstract

In this paper, the Klein–Gordon–Zakharov equations which model the interaction between the Langmuir wave and the ion acoustic wave in a high frequency plasma, are considered. To examine the role played by the nonlinear dispersion term in the formation of solitons, a family of the considered equations with power law nonlinearity are investigated. By using two solitary wave ansatze in terms of sechp(x) and tanhp(x) functions, we find exact analytical bright and dark soliton solutions for the considered model. The physical parameters in the soliton solutions are obtained as function of the dependent model coefficients. The conditions of existence of solitons are presented. These closed form solutions are helpful to well understand the mechanism of the complicated physical phenomena and dynamical processes modeled by the used model.