Trajectory equation of a lump before and after collision with line, lump, and breather waves for (2+1)-dimensional Kadomtsev–Petviashvili equation**Project supported by the National Natural Science Foundation of China (Grant Nos. 11775121, 11805106, and 11435005) and K C Wong Magna Fund in Ningbo University, China.

Abstract

Based on the hybrid solutions to (2+1)-dimensional Kadomtsev–Petviashvili (KP) equation, the motion trajectory of the solutions to KP equation is further studied. We obtain trajectory equation of a single lump before and after collision with line, lump, and breather waves by approximating solutions of KP equation along some parallel orbits at infinity. We derive the mathematical expression of the phase change before and after the collision of a lump wave. At the same time, we give some collision plots to reveal the obvious phase change. Our method proposed to find the trajectory equation of a lump wave can be applied to other (2+1)-dimensional integrable equations. The results expand the understanding of lump, breather, and hybrid solutions in soliton theory.