Diverse high-order soliton solutions and novel hybrid behaviors for the (2+1)-dimensional KP-BBM equation

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