Evolution of multi-solitons and interaction behaviors of lump to a (2+1) dimensional generalized shallow water wave model

Abstract

In this paper, the trajectory equations of 1-lump before and after collision with high-order solitons and the degradation of some novel breather waves are studied in the (2+1)-dimensional generalized Calogero-Bogoyavlenskii-Schiff equation(gCBS). Firstly, we derive N-solitons for the gCBS equation by the Hirota bilinear form. With the help of N-solitons, we obtain M-lump as well as high-order breather based on the long-wave limit technique and the parametric conjugate method. Secondly, we construct many hybrid waves, such as the hybrid wave between breather and lump. Thirdly, the interaction phenomenon of lump-N-solitons(N → ∞) is investigated, and the theory of its existence is given and proved. Besides, the different degeneracies of double and single breather are discussed. Finally, we also present a large number of two-dimensional and three-dimensional images to better illustrate these nonlinear evolutionary behaviors.