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.