Trajectory equation of a lump before and after collision with other waves for generalized Hirota–Satsuma–Ito equation

Abstract

Based on the Hirota bilinear and long wave limit methods, the hybrid solutions of m-lump with n-soliton and n-breather wave for generalized Hirota–Satsuma–Ito (GHSI) equation are constructed. Then, by approximating solutions of the GHSI equation along some parallel orbits at infinity, the trajectory equation of a lump wave before and after collisions with n-soliton and n-breather wave are studied, and the expressions of phase shift for lump wave before and after collisions are given. Furthermore, it is revealed that collisions between the lump wave and other waves are elastic, the corresponding collision diagrams are used to further explain.