In this paper, the semi-rational solutions that causes vector rogue
waves and breathers can be obtained by using the Darboux dressing
transformation. We studied vector rogue waves and the interaction
between rogue waves and light-dark solitons, and observed that during
the interaction, due to the interference between the light-dark
components of the solitons, a respiration-like structures appears.
Besides, it can be observed that the rogue waves and soliton merge
together. Moreover, the main characteristics of the interactions between
the breathers and bright-dark solitons are displayed with some graphics.