Effect of local Peregrine soliton emergence on statistics of random waves in the 1-D focusing Nonlinear Schrödinger equation

Abstract

The Peregrine soliton is often considered as a prototype of the rogue waves. After recent advances in the semi-classical limit of the 1-D focusing Nonlinear Schrödinger (NLS) equation this conjecture can be seen from another perspective. In the present paper, connecting deterministic and statistical approaches, we numerically demonstrate the effect of the universal local appearance of Peregrine solitons on the evolution of statistical properties of random waves. Evidences of this effect are found in recent experimental studies in the contexts of fiber optics and hydrodynamics. The present approach can serve as a powerful tool for the description of the transient dynamics of random waves and provide new insights into the problem of the rogue waves formation.

arXiv comment7 pages, 5 figures

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Cited by in corpus (5)

• Persistence of hydrodynamic envelope solitons: detection and rogue wave occurrence
• Statistics of extreme events in integrable turbulence
• Prediction and manipulation of hydrodynamic rogue waves via nonlinear spectral engineering
• Integrable turbulence developing from strongly nonlinear partially coherent waves
• Spatio-temporal observation of higher-order modulation instability in a recirculating fiber loop