https://doi.org/10.1140/epjp/s13360-024-05080-8
Regular Article
N-soliton, soliton molecules, Y-type soliton, periodic lump and other wave solutions of the new reduced B-type Kadomtsev–Petviashvili equation for shallow water waves
School of Physics and Electronic Information Engineering, Henan Polytechnic University, 454003, Jiaozuo, China
a konka05@163.com, kangjiaw@126.com
Received:
14
August
2023
Accepted:
10
March
2024
Published online:
21
March
2024
In the present work, we aim to look into the new reduced form of the B-type Kadomtsev–Petviashvili equation (gBKPe) for the shallow water waves. First, the N-soliton solutions are constructed via the bilinear form. Based on this, we expound the resonance conditions of the soliton molecules on the 
, 
, 
planes by introducing velocity resonance mechanism and obtain the soliton molecules. Besides, we extract the Y-type soliton solutions through imposing the novel restrictive condition to the N-soliton solutions. Furthermore, we also explore the periodic lump solutions by using the symbolic computation and the ansatz function method. In the end, the Sub-equation approach is exerted to investigate the other wave solutions, which include the singular periodic wave, kinky solitary wave and bright-dark wave solutions. The graphical representations of the obtained solutions are revealed by taking the appropriate parameters. According to the literature known to us, the solutions reported in this research have not been studied elsewhere, which can enlargement the exact solutions of the new reduced form of the gBKPe.
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