Evolutionary behavior of breathers and interaction solutions with M-solitons for (2+1)-dimensional KdV system

By employing the parameter limit method and symbolic computation, we investigate a new lump solution of (2+1)-dimensional Korteweg-de Vries (KdV) system from the double breather solutions. Meanwhile, some new nonlinear phenomena, such as the local oscillations and degeneration behavior of double breather solutions, are studied and shown. What is more, we study the existence theorem of interaction solutions between lump solutions and M-solitons, and give a detailed proof process for the first time. Some concrete examples are presented to verify the effectiveness and correctness of the described theorem. Finally, some spatial structure figures are simulated and displayed to reflect the evolutionary behavior of interaction solution with the change of soliton number M. (C) 2019 Elsevier Ltd. All rights reserved.