Higher-order hybrid rogue wave and breather interaction dynamics for the AB system in two-layer fluids

Abstract

Rogue waves and breathers emerge as significant solitons, result from ubiquitous nonlinear effects of dynamics in the natural world, science and engineering. In this paper, we study the AB system, a model derived from a two-layer fluid that is widely used to investigate nonlinear fluid dynamics. We use the Darboux transformation to construct analytical solutions for higher-order hybrid rogue waves and breathers, which are expressed by symmetric algebraic matrices. We use these solutions and the spectrum parameters to explore the complex interaction dynamics of the hybrid rogue waves and breathers. We find that the interactions cause significant changes in the phases and shapes. Moreover, we discover an interesting phenomenon: the collisions between the rogue waves and breathers are semi-elastic, meaning that only the phases of the rogue waves change, while the speeds, shapes and phases of the breathers remain the same, before and after the collisions. This study provides new insights into the dynamics of the AB system, and helps us understand nonlinear phenomena in various two-layer fluid systems.