Abstract
In this paper, a Wronskian condition and a Grammian condition are proposed for an extended (3+1)-dimensional Jimbo–Miwa equation, which guarantee that the N-soliton solutions of the equation can be expressed in Wronskian and Grammian determinants. Moreover, some examples of Wronskian and Grammian solutions are explicitly computed, and the corresponding soliton dynamics are graphically illustrated via Mathematica by choosing suitable parameters. In addition, the Pfaffianization of the extended (3+1)-dimensional Jimbo–Miwa equation is realized to generate a new coupled (3+1)-dimensional system whose solutions are further expressed as Wronskian-type and Grammian-type Pfaffians.
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