In this paper, a two-dimensional extended version of the nonlinear Schrödinger equation is investigated, which is called Maccari system. This system can compete with Davey–Stewartson equation and \((2+1)\) -dimensional nonlinear Schrödinger equation in describing nonlinear waves. We obtained N-soliton and breather solutions of Maccari system by using the perturbation expansion method. The elastic collision of semi-rational solutions composed of lump, soliton and breather are also derived by taking a long wave limit of the obtained solitons. Furthermore, the inelastic collisions of first-order semi-rational solutions, namely (a) a hybrid of line rogue wave and dark soliton, (b) a hybrid of fusion lump and dark soliton, and (c) a hybrid of fission lump and dark soliton, are presented in terms of the KP hierarchy. Additionally, the semi-rational solutions composed of fusion lump, soliton and fission lump are derived. Simultaneously, the semi-rational solutions, which consist of fusion lump, fission lump, line rogue wave and dark soliton are also derived. The inelastic collisions of high-order semi-rational solutions of Maccari system have been rarely reported in other nonlinear systems.
