A New Generalization of Extended Tanh-Function Method for Solving Nonlinear Evolution Equations**The project supported by National Natural Science Foundation of China under Grant No. 1007201 and the National Key Basic Research Development Project Program under Grant No. G1998030600

Abstract

Making use of a new generalized ansätze and a proper transformation, we generalized the extended tanh-function method. Applying the generalized method with the aid of Maple, we consider some nonlinear evolution equations. 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 the 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.