| Summary: | In this study, under the considerations of symbolic computation with the help of Mathematica software, various types of solitary wave solutions for the (3 + 1)-dimensional Jimo–Miwa (JM) equation are successfully constructed based on the extended modified rational expansion method. The constructed solutions are novel and more general for the JM equation named kink wave solutions, anti-kink wave solutions, bright and dark solutions, mixed solutions in the shape of bright-dark solutions, and periodic waves, which do not exist in the existing literature. The physical phenomena of the demonstrated results is represented graphically by two-dimensional, three-dimensional, and contour images with the help of Mathematica. The obtained results will be widely used to explain the various interesting physical structures in the areas of optics, plasma, gas, acoustics, classical mechanics, fluid dynamics, heat transfer, and many others.
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