Abstract
This paper retrieves new periodic solitary wave solutions for the (3+1)-dimensional extended Jimbo–Miwa equations, based on the Hirota bilinear method, by utilizing Maple software. As a result, the Hirota bilinear method is successfully employed and acquired several classes of solitary wave solutions in terms of a new combination of exponential function, trigonometric function and hyperbolic functions. All solutions have been verified back into its corresponding equation by Maple. We depicted the physical explanation of the extracted solutions with the free choice of the different parameters by plotting some 3D and 2D illustrations. Finally, it has been illustrated that the executed method is robust and more efficient than other methods and the obtained solutions are trustworthy in the applied sciences.
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