New Extended (G′/G)-Expansion Method and its Application in the (3+1)-Dimensional Equation to Find New Exact Traveling Wave Solutions

A new extended (G′/G)-expansion method is presented in this paper to construct more general type and new traveling wave solutions of nonlinear partial differential equations. To illustrate the novelty and advantage of the proposed method, we solve the (3+1)-dimensional Jimbo-Miwa equation. Abundant exact traveling wave solutions of this equation is obtained, which successfully recover most of the previously published solutions. Many of those solutions are found for the first time. Furthermore, the results reveal that the proposed method is very elementary, effective and can be used for many other nonlinear partial differential equations.