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/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.

arXiv comment9 figures, accepted in PRE

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Cited by in corpus (3)

• General rogue waves in the nonlocal PT-symmetric nonlinear Schrodinger equation
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• Bound-state soliton gas as a limit of adiabatically growing integrable turbulence