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Emergent rogue wave structures and statistics in spontaneous modulation instability.

Shanti Toenger¹, Thomas Godin¹, Cyril Billet¹

¹Institut FEMTO-ST, UMR 6174 CNRS-Université de Franche-Comté, Besançon, France.

Scientific Reports

|May 21, 2015

Summary

Noise-seeded modulation instability (MI) in the nonlinear Schrödinger equation (NLSE) generates localized waves. Numerical simulations show these waves closely match NLSE analytic solutions, suggesting rogue waves arise from soliton collisions, not Peregrine solitons.

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Area of Science:

Nonlinear physics
Wave phenomena
Computational physics

Background:

The nonlinear Schrödinger equation (NLSE) models wave packet evolution in dispersive media.
Modulation instability (MI) in the NLSE can generate localized nonlinear waves like breathers and solitons on finite background (SFB).
The emergence of rogue waves from noise via MI is not fully understood, particularly how well analytic NLSE solutions describe these structures.

Purpose of the Study:

To investigate the characteristics of localized structures emerging from noise-seeded modulation instability (MI) in the NLSE.
To compare numerically simulated emergent peaks with known analytic solutions of the NLSE.
To clarify the nature of rogue waves in the context of NLSE solutions.

Main Methods:

Numerical simulations of the nonlinear Schrödinger equation (NLSE) with noise-seeded initial conditions.
Generation of a large ensemble of emergent peaks from chaotic MI.
Comparison of the statistical properties of simulated peaks with analytic NLSE solutions, including elementary breathers and higher-order SFB structures.

Main Results:

Noise-seeded MI produces both elementary breather and higher-order soliton on finite background (SFB) structures.
The statistical properties of noise-induced peaks closely align with analytic NLSE predictions.
The Peregrine soliton is unlikely to be a rogue wave prototype.

Conclusions:

Analytic NLSE solutions, specifically SFB structures, accurately model localized waves generated by noise-seeded MI.
Rogue waves in the NLSE are best understood as resulting from collisions between elementary SFB solutions.
The study revisits the role of the Peregrine soliton as a rogue wave prototype.