Nonlinear superposition and trajectory equations of lump soliton with other nonlinear localized waves for (2+1)-dimensional nonlinear wave equation

Based on the Hirota bilinear method and the long wave limit method, this paper explores the novel nonlinear superposition among kink wave, lump wave and other waves for the (2+1)-dimensional nonlinear wave equation under the conditions of \(\lambda _3 = 0\) ${\lambda }_3=0$ and \(\lambda _4 = 0\) ${\lambda }_4=0$ . Furthermore, when \(\lambda _3 \ne 0\) ${\lambda }_3\ne 0$ and \(\lambda _4 \ne 0\) ${\lambda }_4\ne 0$ , the trajectory equations, phase shift, height and depth of a lump wave before and after collision with 1-kink wave, 2-kink waves and 1-breather wave are obtained by approximating the solution of the (2+1)-dimensional nonlinear wave equation along certain parallel orbits at infinity. Finally, the above situation was further extended to the interaction between lump waves, n-kink waves and n-breather waves, and specific vivid graphics were provided.