Statistics of Vector Manakov Rogue Waves

TL;DR

This paper analyzes the statistical properties of rogue waves in the Manakov system, linking their formation mechanisms to their statistical signatures and proposing new criteria for identifying these extreme events.

Contribution

It introduces a statistical framework for classifying rogue waves in the Manakov system and connects their formation mechanisms to their statistical characteristics.

Findings

Analytical solutions are the main high amplitude events.

High amplitude events originate from modulation instability.

Interaction among events influences rogue wave creation.

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/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 relation between the type of the 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 new 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 defining new criteria for identifying RW events.