The modified simple equation method and its applications to (2+1)-dimensional systems of nonlinear evolution equations

Abstract

The modified simple equation method is employed to find the exact traveling wave solutions involving parameters for nonlinear systems of evolution equations via the (2+1)-dimensional Konopelchneko-Dubrovsky equations and the (2+1)-dimensional Nizhnik-Novikov-Vesselov equations in two dimensions. When these parameters are taken to be special values, the solitary wave solutions are derived from the exact traveling wave solutions. It is shown that the modified simple equation method provides an effective and a more powerful mathematical tool for solving nonlinear evolution equations in mathematical physics. Comparison between our results and the well-known results will be presented. Key words: Modified simple equation method, Konopelchneko-Dubrovsky equations, Nizhnik-Novikov-Vesselov equations, exact traveling solutions, solitary wave solutions.