New exact solutions for some nonlinear differential equations using symbolic computation

Based on computerized symbolic computation and a new, general ansatze, 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. (C) 2003 Elsevier Inc. All rights reserved.