A study on resonant collision in the two-dimensional multi-component long-wave–short-wave resonance system

Abstract

This study focuses on the occurrence and dynamics of resonant collisions of breathers among themselves and with rational solitary waves in a two-dimensional multi-component long-wave–short-wave resonance system. These nonlinear coherent structures are described by a family of semi-rational solutions encompassing almost all known solitary waves with non-zero boundary conditions. In the case of resonant collision of parallel breathers, the original breathers split up into several new breathers or combine into a new breather. They also exhibit a mixed behaviour displaying a mixture of splitting and recombination processes. The lumps and line rogue waves—two distinct forms of rational solitary waves—can undergo partial and complete resonant collisions with breathers. In the partial resonant collisions, the lumps do not exit well before interaction but suddenly emerge from the breathers and finally keep existing for an infinite time after interaction, or they alter from existence to annihilation as one moves fromt→−∞tot→+∞. The line rogue waves arise and decay along ray waves instead of line waves. In the complete resonant collisions, the lumps first detach from breathers and then fuse into other breathers, while the line rogue waves appear and disappear along line segment waves of finite length, namely, both of the lumps and rogue waves are doubly localized in two-dimensional space as well as in time.