Resonant Y-shape soliton, X-shape soliton, breather wave and abundant travelling wave solutions to the generalised (3+1)-dimensional B-type Kadomtsev–Petviashvili equation

This exploration aims to extract some new exact solutions of the (3+1)-dimensional B-type Kadomtsev–Petviashvili equation (BKPE) that plays a significant role in fluid dynamics. Based on the N-soliton solutions extracted by the Hirota bilinear method, the Y-shape and X-shape soliton solutions and the breather wave solutions are derived by assigning resonant conditions and conjugate conditions, respectively. Furthermore, three powerful tools, namely the Bernoulli sub-equation function method, Wang’s direct mapping method-II and Kudryashov method, are employed to explore the diverse travelling wave solutions, which includes the kink solitary wave, anti-kink solitary wave, periodic wave and singular wave solutions. The wave structures of the attained solutions are displayed as diagrams using Maple. As we all know, the outcomes presented in the study are all brand new and have not been reported in other work, which can enable us to better understand the dynamic behaviours of the considered equation.