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Abstract
In this paper, we study the general lump-type solutions of the (3+1)-dimensional Jimbo–Miwa equation via Hirota bilinear method and the ansatz technique. In contrast with lump solutions presented before, we firstly find a general quadratic function solution of the transformed bilinear Jimbo–Miwa equation and then expand it as the sums of squares of linear functions to satisfy analyticity condition. Especially, we get a lump-type solution with fifteen parameters which possess eleven arbitrary independent parameters and four constraint conditions. This solution supplements the existing lump-type solutions obtained previously in the literature. Finally, we conclude that there are only two linearly independent non-constant linear functions in the summation for a positive quadratic function solution.
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