Symbolic computation and families of Jacobi elliptic function solutions of the (2Â +Â 1)-dimensional Nizhnik-Novikov-Veselov equation

In this paper, with the aid of the symbolic computation we have improved the extended F-expansion method in [Chaos, Solitons and Fractals 22 (2004) 111] and proposed the further improved F-expansion method. By this method, we have gotten many new exact solutions which we have never seen before within our knowledge of the (2 + 1)-dimensional Nizhnik-Novikov-Veselov equations. In addition,the solutions we get are more general than the solutions the extended F-expansion method gets. At the same time, our method is more convenient than the method in [Chaos, Solitons and Fractals 18 (2003) 299-309] and the solutions we get are more abundant than the solutions in [H-q Zh. Appl. Math. E-Notes 1 (2001) 139]. In other word, the solutions in [H-q Zh. Appl. Math. E-Notes 1 (2001) 139] are part of our solutions. Our method can also apply to other partial differential equations and also get many new exact solutions.