New exact solutions for some nonlinear differential equations using symbolic computation

Abstract

Based on computerized symbolic computation and a new general ansätze, a generalized tanh-function method for constructing multiple travelling wave solutions of nonlinear evolution equations (NEEs) is presented and implemented in a computer algebraic system. Applying the generalized method, with the aid of Maple, we consider some NEEs with physics interests. As a result, we can successfully recover the previously known solitary wave solutions that had been found by the extended tanh-function method and other more sophisticated methods. More importantly, for some equations, we also obtain other new and more general solutions at same time. The results include kink-profile solitary-wave solutions, bell-profile solitary-wave solutions, periodic wave solutions, rational solutions, singular solutions and new formal solutions. The properties of the new soliton solutions for WBK equations are shown by some figures.