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In this paper, a (3 + 1)-dimensional B-type Kadomtsev–Petviashvili (BKP) equation is investigated and its various new interaction solutions among solitons, rational waves and periodic waves are obtained by the direct algebraic method, together with the inheritance solving technique. The results are fantastic interaction phenomena, and are shown by figures. Meanwhile, any higher order interaction solutions among solitons, breathers, and lump waves are constructed by an  N -soliton decomposition algorithm developed by us. These innovative results greatly enrich the structure of the solutions of this equation.

Multiwave interaction solutions for a (3 + 1)-dimensional B-type Kadomtsev–Petviashvili equation in fluid dynamics