The modified trial equation method to the (2+1)-dimensional Broer-Kaup-Kupershmidt equation and Kolmogorov-Petrovskii-Piskunov equation

Abstract

Many methods have been developed by scientists to find solutions for nonlinear problems. In this paper, the general structure of the modified trial equation method (MTEM) is introduced, and MTEM is used to find some exact solutions of (2+1)-dimensional Broer-Kaup-Kupershmidt (BKK), Kolmogorov-Petrovskii-Piskunov (KPP) equations. Firstly, an algebraic equation system is obtained by reducing the nonlinear partial differential equation (NLPDE) to the ordinary differential equation under the travelling wave transformation. Travelling wave solutions are found by solving the obtained algebraic equation systems. By using Mathematica 9 program, three and two dimensional graphs for suitable parameters were plotted to analyze the physical behavior of wave solutions. MTEM is of great importance in finding exact solutions of some partial differential equations.