The Fission, Fusion and Annihilation of Solitons of the (2+1)-Dimensional Broer-Kaup-Kupershmidt System

The interactions between soliton solutions of integrable models are usually considered to be completely elastic. That is to say, the amplitude, velocity and wave shape of solitons are not changed after nonlinear interaction [1]. However, for some specific solutions of some (2+1)-dimensional models, the interactions among solitonic excitations are not completely elastic since their shapes are changed after their collisions [2]. Furthermore, for some nonlinearmodels, two or more solitons may fuse into one soliton at a specific time, while sometimes one soliton may fission into two or more solitons at another specific time [3]. These phenomena are often called soliton fusion and soliton fission, respectively, and have been observed in many kinds of physical systems such as some organic membranes and macromolecular materials [4], and in many physical fields like plasma physics, nuclear physics and hydrodynamics [5]. Recently, Wang et al. [6] first discussed two (1+1)-dimensional models, the Burgers equation and Sharma-Tasso-Olver (STO) equation, via Hirota’s direct method and the Bäcklund transformation, and found the soliton fission and soliton fusion phenomenas. Furthermore, Ma and Zheng [7] also fond these phenomena in the (2+1)-dimensional Higher-Order-Broer-Kaup (HBK) system. Along this line, in this paper, we further study the soliton fission, soliton fusion phenomena and the annihilation of solitons in the following celebrated (2+1)-dimensional Broer-Kaup-Kupershmidt (BKK) system [8]: