By applying the binary bell polynomial scheme, the bilinear form, Bäcklund Transformations, and lax pairs of an extended (3+1)-dimensional Jimbo-miwa (JM) equation are constructed. Next, periodic wave-type solutions can also be obtained to the extended (3+1)-dimensional JM equation through the three-wave method with the help of maple. Finally, a test function of the sech-function method is utilized to get solitary waves of this study problem. These new results can help us better understand interesting physical phenomena and mechanism. KEYWORDS binary bell polynomial scheme, extended (3+1)-dimensional JM equation, bäcklund transformations and Lax pairs, periodic wave-Type solutions, Solitary Waves MSC CLASSIFICATION 35L05; 35C08; 35Q35 This equation was firstly proposed by A. M. Wazwaz to study its one-soliton solution, two-soliton solution, and multi-soliton solutions of Equation (1) by utilizing the simplified Hirota bilinear method. 25 Meanwhile, Sun and Chen obtained the lump solutions of Equation (1). 26 Manafian 27 used the Hirota bilinear method of a new combination of exponential function, trigonometric function, and hyperbolic functions to obtain new periodic solitary wave solutions, etc. 27-29
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