New traveling wave solutions for higher dimensional nonlinear evolution equations using a generalized -expansion method

Abstract

In this paper, we construct new traveling wave solutions of some nonlinear evolution equations in mathematical physics via the (3+1)-dimensional potential-YTSF equation, the (3+1)-dimensional modified KdV–Zakharov–Kuznetsev equation, the (3+1)-dimensional Kadomtsev–Petviashvili equation and the (1+1)-dimensional KdV equation by using a generalized -expansion method, where G = G(ξ) satisfies the Jacobi elliptic equation [G′(ξ)]2 = P(G). Here, we assume that P(G) is a polynomial of fourth order. Many new exact solutions in terms of the Jacobi elliptic functions are obtained.