Some applications of the modified (G ′ /G 2 )-expansion method in mathematical physics

Abstract

This study proposes a modified (G ′ /G 2 )-expansion method to seek new more general exact traveling wave solutions to nonlinear evolution equations (NLEEs). To demonstrate the validity of this method, two interesting NLEEs are considered: the (2 + 1)-dimensional typical breaking soliton equation and (1 + 1)-dimensional classical Boussinesq system of equations. Consequently, we construct some new exact solutions involving the free parameters of the considered equations, which are categorized into three unique forms including rational, periodic, and hyperbolic functions. Thus, this study illustrates the effectiveness and the simplicity of the proposed method with the aid of symbolically computational software such as MATHEMATICA.