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A $$(3+1)$$ ( 3 + 1 ) -dimensional B-type Kadomtsev–Petviashvili equation, which can be applied to describe the propagation of non-linear waves in fluid dynamics, is under investigation in this paper. Based on the binary Bell polynomials, Hirota method, and symbolic computation, the bilinear form is obtained. Bäcklund transformations are derived in the Bell-polynomial and bilinear forms...
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