Nonlinear localized waves and their interactions for a (2+1)-dimensional extended Bogoyavlenskii-Kadomtsev–Petviashvili equation in a fluid

Abstract

In fluid dynamics, a (2+1)-dimensional extended Bogoyavlenskii-Kadomtsev-Petvi-ashvili equation is hereby investigated. Bilinear form and N-soliton solutions are determined with the Hirota method, where N is a positive integer. N-soliton solutions are used to build the higher-order breather and lump solutions with the complex parameter relation and long-wave-limit method. Elastic and inelastic interactions between the two breathers and elastic interaction between the two lumps are constructed and graphically depicted. We find that the coefficients of the weak dispersion terms have an effect on the velocities and amplitudes of the breathers and lumps. Based on the hybrid solutions containing the breathers, lumps and solitons, several interactions of those nonlinear localized waves are graphically illustrated, including the fission of the breather and soliton, elastic or inelastic interaction between the one breather and one soliton, elastic interaction among one breather and two solitons, as well as elastic interaction between the one lump and one breather.