Diverse higher-order soliton solutions and novel hybrid behaviours of the (2+1)-dimensional KP-BBM equation

This paper is devoted to the study of higher-order soliton solutions and some hybrid behaviours between them in the (2 + 1)-dimensional Kadomtsev-Petviashvili-Benjamin-Bona-Mahony (KP-BBM) equation. Firstly, we obtain a new lump solution by studying the degenerate behaviour of the breathers. Secondly, we focus on studying the N-soliton solutions, higher-order breathers and higher-order lump solutions by using the long-wave limit method. Some novel higher-hybrid behaviours are studied to show the effect of the superposition of different solitons on the structure of the solution, such as the hybrid behaviours between the m-lump solution and n-soliton, the hybrid behaviours between the 1-breather solution and n-soliton. Finally, many three-dimensional images and density projections of spatial structures are displayed to reflect the evolutionary behaviour of the higher-order soliton solutions with the increase of order number.