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

A multiple exp-function method for exact multiple wave solutions of nonlinear partial differential equations is proposed. The method is oriented towards the ease of use and capability of computer algebra systems and provides a direct and systematic solution procedure that generalizes Hirota's perturbation scheme. With the help of Maple, applying the approach to the (3 + 1)-dimensional potential-Yu-Toda-Sasa-Fukuyama equation yields exact explicit one-wave, two-wave and three-wave solutions, which include one-soliton, two-soliton and three-soliton type solutions. Two cases with specific values of the involved parameters are plotted for each of the two-wave and three-wave solutions.