Dynamics of multi-breathers, N-solitons and M-lump solutions in the (2+1)-dimensional KdV equation

摘要

The (2+1)-dimensional Korteweg-de Vries (KdV) equation is studied by distinct methods. The parameter limit method is used to derive multi-breathers solutions and lump solutions with different structures. The Hirota's bilinear method is used to obtain N-soliton solutions, N-order rational solutions and M-lump solutions. Besides, we also analyze parametric reasons for the degradation of breathers solutions and emergence of different lump solutions, and simulate the different structures of the exact solutions obtained in this paper by using three-dimensional images.