General semi-rational solutions in the (2+1)-dimensional three-wave resonant interactions

Abstract

In this paper, we study the general semi-rational solutions of the (2+1)-dimensional three-wave resonant interactions via the Hirota’s bilinear method and Kadomtsev–Petviashvili (KP) reduction method. There exist plenty of novel collision behaviors of nonlinear waves in the systems. The collision behaviors mainly contain the resonant collisions and elastic collisions between rational waves, multi-line-solitons and multi-breathers. The resonant collisions are divided into the partial and complete resonant collisions determined by the localization features of the waves in time evolution. Partial resonant collision describes the fission, fussion processes of rational waves in the line-soliton or breather backgrounds, which is semi-localized in time. Complete resonant collision describes the rational waves appearing and disappearing in the multi-line-soliton or multi-breather backgrounds for a short time, which is fully localized in time. The elastic collision is a passable propagation behavior remaining shape and amplitude in time evolution. Furthermore, we also display the interaction behaviors of multi-breathers among themselves and with multi-line-solitons. These results greatly enrich the dynamics of nonlinear waves in the semi-rational solutions for high-dimensional nonlinear interaction systems.