Statistics of vector Manakov rogue waves

Abstract

We present a statistical analysis based on the height and return-time probabilities of high-amplitude wave events in both focusing and defocusing Manakov systems. We find that analytical rational or semirational solutions, associated with extreme, rogue wave (RW) structures, are the leading high-amplitude events in this system. We define the thresholds for classifying an extreme wave event as a RW. Our results indicate that there is a strong relationship between the type of RW and the mechanism which is responsible for its creation. Initially, high-amplitude events originate from modulation instability. Upon subsequent evolution, the interaction among these events prevails as the mechanism for RW creation. We suggest a strategy for confirming the basic properties of different extreme events. This involves the definition of proper statistical measures at each stage of the RW dynamics. Our results point to the need for redefining criteria for identifying RW events.