A multiple exp-function method for nonlinear differential equations and its application

Abstract

A multiple exp-function method to exact multiple wave solutions of nonlinear\npartial differential equations is proposed. The method is oriented towards ease\nof use and capability of computer algebra systems, and provides a direct and\nsystematical solution procedure which generalizes Hirota's perturbation scheme.\nWith help of Maple, an application of the approach to the $3+1$ dimensional\npotential-Yu-Toda-Sasa-Fukuyama equation yields exact explicit 1-wave and\n2-wave and 3-wave solutions, which include 1-soliton, 2-soliton and 3-soliton\ntype solutions. Two cases with specific values of the involved parameters are\nplotted for each of 2-wave and 3-wave solutions.\n