Exact solutions of the coupled Higgs equation and the Maccari system using He’s semi-inverse method and [formula omitted]-expansion method

Abstract

In this paper, we establish exact solutions for complex nonlinear equations. The He’s semi-inverse and the ( G ′ G ) -expansion methods are used to construct exact solutions of these equations. We apply He’s semi-inverse method to establish a variational theory for the coupled Higgs equation and Maccari system. Based on this formulation, a solitary solution can be easily obtained using the Ritz method. The ( G ′ G ) -expansion method is used to seek more general exact solutions of the coupled Higgs equation and the Maccari system. As a result, hyperbolic function solutions, trigonometric function solutions and rational function solutions with free parameters are obtained. When the parameters are taken as special values the solitary wave solutions are also derived from the traveling wave solutions. Moreover, it is observed that the suggested technique is compatible with the physical nature of such problems.