New traveling wave solutions for higher dimensional nonlinear evolution equations using a generalized \((\frac{G'}{G})\)-expansion method. (English) Zbl 1170.35310
Summary: 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 \((\frac{G'}{G})\)-expansion method, where \(G=G(\xi)\) satisfies the Jacobi elliptic equation \([G'(\xi)]^2= P(G)\). 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.
MSC:
35A25 | Other special methods applied to PDEs |
35Q53 | KdV equations (Korteweg-de Vries equations) |
35C05 | Solutions to PDEs in closed form |