New Soliton Solutions and Trajectory Equations of Soliton Collision to a (2+1)-Dimensional Shallow Water Wave Model

The motivation of this paper is to investigate some new soliton solutions and the trajectory problem of hybrid behavior for the (2+1)-dimensional Hirota-Satsuma-Ito equation. Firstly, based on the bilinear form and a new test function, a novel soliton solution and lump solution are obtained by employing parameter limit method. Secondly, based on Hirota’s direct method and the long-wave limit method, the N-soliton solution, the high-order breather solution and the high-order lump solution are studied. More importantly, we studied the trajectory equations of lump solutions before and after collisions with some different solitons, such as collisions between l-lump and N solitons ( \(N = 1,2\) $N=1,2$ ), and collisions between l-lump and breathers. We also used a large number of two-dimensional and three-dimensional plots to display the results of the paper’s research.