Trajectory equation of a lump before and after collision with other waves for (2+1)-dimensional Sawada–Kotera equation

In this paper, we employ the Hirota bilinear and long wave limit methods to obtain the hybrid solutions consisting of mth order lumps and nth order breathers, mth order lumps and n line waves for (2+1)-dimensional Sawada–Kotera (SK) equation. Then, according to the characteristics of a lump wave moving along a straight line, the trajectory equation of a lump before and after collision with a line wave, two line waves and breather waves are obtained by approximating the solution of SK equation along some parallel orbits at infinity. Furthermore, we generalize the above cases to the collision of a lump wave with n line waves and the nth order breather waves, and the corresponding trajectory equations are presented. We also give the expression of phase shift for the lump wave, and verify that when ϑi≠0, the height of the lump wave before and after collision does not change, which reveals that collisions between a lump and other waves are elastic.