Trajectory equations of interaction and evolution behaviors of a novel multi-soliton to a (2+1)-dimensional shallow water wave model

Based on a new bilinear equation, we investigated some new dynamic behaviors of the (2+1)-dimensional shallow water wave model, such as hybridization behavior between different solitons, trajectory equations for lump collisions, and evolution behavior of multi-breathers. Firstly, the N-soliton solution of Ito equation is studied, and some high-order breather waves can be obtained from the N-soliton solutions through paired-complexification of parameters. Secondly, the high-order lump solutions and the hybrid solutions are obtained by employing the long-wave limit method, and the motion velocity and trajectory equations of high-order lump waves are analyzed. Moreover, based on the trajectory equations of the higher-order lump solutions, we give and prove the trajectory theorem of 1-lump before and after interaction with n-soliton. Finally, we obtain some new lump solutions from the multi-solitons by constructing a new test function and using the parameter limit method. Meanwhile, some evolutionary behaviors of the obtained solutions are shown through a large number of three-dimensional graphs with different and appropriate parameters.