The generalized (3 + 1)-dimensional B-type Kadomtsev–Petviashvili equation: resonant multiple soliton, N-soliton, soliton molecules and the interaction solutions

The main orientation of the current research is to look into the generalized (3 + 1)-dimensional B-type Kadomtsev–Petviashvili equation (BKPE) for the water waves. By exerting the Cole-Hopf transform, we extract its Hirota bilinear equation. First, the weight algorithm (WA) together with the linear superposition principle(LSP) is carried out to look for the resonant multiple soliton solutions (RMSSs). Two different types of the RMSSs are obtained by introducing the parameterization of the wave numbers and frequencies. Second, the N-soliton solutions (NSSs) are also explored by using Hirota bilinear equation. On this basis, the resonance conditions of the soliton molecules on the (x, y)-, (x, z)- and (y, z)-planes are extracted and the soliton molecules are found. Finally, the ansatz function scheme, together with the symbolic computation is manipulated to look into the interaction solutions (ISs). Two different interaction solutions of the sin-cosh type and cos-cosh type are developed. A comparison between the RMSSs and the N-soliton solutions are elaborated in detail. Additionally, the dynamics of the solutions are displayed graphically to expound the physical interpretation. The proposed methods in this work can be also employed to inquire into the similar exact solutions of the other PDEs.