Abstract
In this paper, the localized solutions of the (2+1)-dimensional B-Kadomtsev–Petviashvili (BKP) equation, which is a useful physical model, are further studied. Firstly, by using the theory of Hirota bilinear operator, the corresponding N-soliton solutions are obtained. Then the localized solutions, which are the M-lump solutions, higher-order breathers and hybrid solutions, are also constructed by taking a long-wave limit and introducing some conjugation conditions. In the meanwhile, the dynamic behaviors of these obtained solutions are analyzed and shown graphically by the corresponding numerical simulations with specific parameters, which can greatly affect the solutions, such as the propagation properties.
•Using Hirota bilinear method, N-soliton solutions are obtained.•Using long-wave limit, M-lumps, breathers, hybrid solutions are derived.•Dynamic properties are analyzed and illustrated.