Lump and interaction dynamics of the (2+1)-dimensional Bogoyavlenskii–Kadomtsev–Petviashvili equation

Abstract

This paper mainly considers the (2+1)-dimensional Bogoyavlenskii–Kadomtsev–Petviashvili equation describing propagation dynamics of nonlinear waves appearing in physics, biology and electrical networks. A simple method to derive the multiple lumps and lump molecules is proposed by means of the solutions of Grammian form and polynomial functions. The interaction dynamical behaviors of the lumps and lump molecules are analyzed with the aid of numerical simulation. The interaction solutions including lumps, lump molecules and kink solitons are obtained, where the lumps can be emitted and absorbed by solitons. The phenomenon that one lump wave exchanges between two bound solitons is presented. A special Grammian τ-function is employed to construct the lump chain. Based on an analytical method related to dominant domain, we systematically analyze the interactions between lump chain and solitons. The lump chain can be emitted by a soliton and then absorbed by other solitons when the parameter is in a certain range. A large number of new solutions obtained in this paper are helpful to study the wave phenomena existing in the theory of water wave, soliton, optical fiber communication and other relevant scientific fields.