Formula omitted]-lump and hybrid solutions of a generalized (2+1)-dimensional Hirota–Satsuma–Ito equation

Abstract

In this paper, the N-soliton solutions of a generalized (2+1)-dimensional Hirota–Satsuma–Ito equation are obtained by means of the bilinear method. By applying the long wave limit to the N-solitons, the M-lump waves are constructed. The propagation orbits, velocities and the collisions among the lumps of the M-lump waves are analyzed. Three kinds of high-order hybrid solutions are presented, which contain the hybrid solution between lumps and solitons, a 1-lump and 1-breather, and a m-breather and n-soliton. The results are helpful to explain some nonlinear phenomena of the generalized shallow water wave model.