Exact Solutions of an Extended Jimbo-Miwa Equation by Three Distinct Methods

Abstract

In this article, we focus on exact traveling wave solutions to an extended Jimbo-Miwa equation, which is an extension of the Jimbo-Miwa equation. First, an improved $\left(G^{\prime }/G\right)$ -expansion method, extended $\left(G^{\prime }/G\right)$ -expansion method, and improved two variable ( $\left({\phi }^{\prime }/\phi \right)$ , $\left(1/\phi \right)$ ) expansion method are introduced. Second, with these introduced methods, many new exact traveling wave solutions of EJM equation are constructed, including hyperbolic function solutions, trigonometric function solutions, and rational function solutions which contain many different parameters. Finally, we depict the physical explanation of the extracted solutions with the free choice of the different parameters by plotting some 3D and 2D illustrations. To the best of our knowledge, the received results have not been reported in other studies on the new extended JM equations. We hope that our results can help enrich the study of this new equation.