New exact solutions for three nonlinear evolution equations

By using the general solutions of a coupled Riccati equations and the relations between them a direct algebra method is described to construct several kinds of closed-form travelling wave solutions for some nonlinear differential equations. By this method three important nonlinear partial differential equations are studied and, in addition to rederiving all known solutions, several new solutions are explicitly obtained with the aid of symbolic computation. (C) 2002 Elsevier Science B.V. All rights reserved.