Interaction between Breathers and Rogue Waves in a Nonlinear Optical Fiber

We study the interaction between breather and N-order rogue waves in a nonlinear optical fiber. The impacts of the relative phase and the interaction distance between breathers and rogue waves are discussed in detail. Specifically, the breather can reduce the maximum hump value of high-order rogue waves greatly in the cases of nonzero relative phase or nonzero interaction distance. The characteristic of exclusion between breathers and rogue waves is described qualitatively in the situation of different interaction distances, which can be used to change the temporal-spatial distribution of rogue waves. Their interaction properties are characterized by the trajectory of localized waves' valleys and humps. It is shown that the interaction changes the dynamical evolution trajectory of rogue waves and breathers. These results provide some possible ways to control high-order rogue waves.