Bäcklund transformations and soliton solutions for a $$(3+1)$$ ( 3 + 1 ) -dimensional B-type Kadomtsev–Petviashvili equation in fluid dynamics

摘要: A $$(3+1)$$ -dimensional B-type Kadomtsev–Petviashvili equation, which can be applied to describe the propagation of non-linear waves in fluid dynamics, is under investigation this paper. Based on binary Bell polynomials, Hirota method, and symbolic computation, bilinear form obtained. Backlund transformations are derived Bell-polynomial forms. Besides, one- two-soliton solutions presented. The only coefficient equation affect soliton structure. Soliton shapes keep unchanged after elastic interaction they maintain their original directions amplitudes except for some phase shifts.