Investigation of Exact Solutions of Nonlinear Evolution Equations Using Unified Method

Abstract

In this article, an analytical technique based on unified method is applied to investigate the exact solutions of non-linear homogeneous evolution partial differential equations. These partial differential equations are reduced to ordinary differential equations using different traveling wave transformations, and exact solutions in rational and polynomial forms are obtained. The obtained solutions are presented in the form of 2D and 3D graphics to study the behavior of the analytical solution by setting out the values of suitable parameters. The acquired results reveal that the unified method is a suitable approach for handling non-linear homogeneous evolution equations.

Keywords

• exact solutions
• unified method (UM)
• generalized regularized long wave (<i>GRLW</i>) equation
• modified Zakharov–Kuznetsov equation (<i>mZK</i>)
• traveling wave transformations