Abstract
We demonstrate a simple cascade mechanism that drives the formation and emergence of rogue waves in the generalized non-linear Schr\"{o}dinger equation with third-order dispersion. This conceptually novel generation mechanism is based on inelastic collisions of quasi-solitons and is well described by a resonant-like scattering behaviour for the energy transfer in pair-wise quasi-soliton collisions. Our results demonstrate a threshold for rogue wave emergence and the existence of a period of reduced amplitudes - a "calm before the storm" - preceding the arrival of a rogue wave event. Comparing with ultra-long time window simulations of $3.865\times 10^{6}$ps we observe the statistics of rogue waves in optical fibres with an unprecedented level of detail and accuracy, unambiguously establishing the long-ranged character of the rogue wave power-distribution function over seven orders of magnitude.
Highlights
Reports of "monster" or "freak" waves [1,2,3] on the earth’s oceans have been seen largely as sea men’s tales [4, 5]
We see that the agreement for probability distribution function (PDF) is excellent taking into account that we have reduced the full integration of the generalized non-linear Schrödinger equations (gNLSE) to only discrete collision
Our results emphasize the crucial role played by quasi-soliton interactions in the energy exchange underlying the formation of rogue waves (RW) via the proposed cascade mechanism
Summary
Reports of "monster" or "freak" waves [1,2,3] on the earth’s oceans have been seen largely as sea men’s tales [4, 5]. The recent availability of reliable experimental observations [4, 6] has proved their existence and shown that these "rogues" are rare events [7], governed by long tails in their probability distribution function (PDF) [8], and concurrent with very large wave amplitudes [9, 10] As both deep water waves in the oceans and optical waves in fibres can be described by similar generalized non-linear Schrödinger equations (gNLSE) they both show rogue waves (RW) and long-tail statistics [8, 11, 12].
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