The modified multiple ( G ′ / G $G^{\prime }/G$ )-expansion method and its application to Sharma–Tasso–Olver equation

Abstract

The modified multiple (\(G^{\prime }/G\))-expansion method is proposed in this paper to construct exact solutions of nonlinear evolution equations. The validity and advantage of the proposed method are illustrated by its application to the Sharma–Tasso–Olver equation. As a result, various exact solutions including hyperbolic functions, trigonometric functions and their mixture with parameters are obtained. When some parameters are taken as special values, the known double solitary-like wave solutions are derived from the double hyperbolic function solution. It is shown that the method introduced in this paper has general significance in searching for exact solutions to the nonlinear evolution equations.