RETRACTED ARTICLE: The homogeneous balance method and its applications for finding the exact solutions for nonlinear equations

Abstract

The main objective of this paper is to solve non-linear equations for engineering and science applications. Various emerging engineering and science applications are using non-linear equation to represent the entire problem. Several earlier research works have been focused on solving linear and non-linear equation using different methods but they are application based. In recent days applications are described and represented mathematically in accordance to the non-linear, discreate and non-discrete data. Few research works have used homogeneous balance method for solving multi-dimension equations. Some of the earlier approaches have used homogeneous balance method for investigating WBKL, Kaup–Kupershmidt, and CSNLPD equations, whereas all the methods are not complexity reduced. In order to provide a complexity reduced, fast and highly suitable method for solving non-linear equations representing recent engineering applications. Also, it is well known that the homogeneous balance method is a powerful technique to symbolically compute traveling wave solutions of some nonlinear wave and evolution equations. Hence, in this paper the exact solutions of Gardner equation and Burgers equation are obtained by using homogeneous balance method and verified using MATHEMATICA.