New exact solutions to the coupled (n + 1)-dimensional Klein–Gordon–Zakharov equation with power law nonlinearities

Abstract

In this paper, a special class of exact solutions of the coupled higher-dimensional Klein–Gordon–Zakharov (KGZ) equation with power law nonlinearities is constructed explicitly by separation transformation method. One merit of this work is that when the dimension is larger than one, there is an arbitrary function [Formula: see text], which is used to search for more general exact solutions of the coupled higher-dimensional KGZ equation. As a result, the Jacobi elliptic function solutions and soliton solutions with free parameters are derived, which lead to rich localized nonlinear structures of the coupled higher-dimensional KGZ equation with power law nonlinearities.