Effect of local Peregrine soliton emergence on statistics of random waves in the one-dimensional focusing nonlinear Schrödinger equation

Tikan, Alexey

doi:10.1103/physreve.101.012209

Cited by 27 publications

(26 citation statements)

References 55 publications

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“…2, high-amplitude structures locally similar to PS are found where the kurtosis of the surface elevation κ reaches its maximal value. This fact was recently reported from numerical simulations [36], and we thus provide its first experimental demonstration. As the steepness is increased, the PS no longer fits the typical shape of such events, that nonetheless still emerge where the kurtosis peaks.…”

Section: Discussionsupporting

confidence: 83%

“…Result (i), derived by Bertola and Tovbis, predicts that the gradient catastrophe is regularized by structures that can be locally fitted by a PS [35]. Result (ii), obtained numerically, demonstrates that the emergence of these structures connects to the overshoot of the kurtosis [36]. Whereas result (i) has already been verified numerically and qualitatively in experiments [26,32,36], result (ii) has yet to be investigated experimentally.…”

Section: Introductionmentioning

confidence: 82%

“…Our study shows that this prediction of the NLSE requires extremely small steepnesses. Following a recent numerical study [36], we also carry out the first experimental investigation of the link between the kurtosis of the surface elevation and the emergence of Peregrine-like structures. The correlation between these two quantities is extremely robust and persists for steepnesses as high as 0.1 for which wave breaking occurs.…”

Section: Discussionmentioning

confidence: 99%

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Emergence of Peregrine solitons in integrable turbulence of deep water gravity waves

Michel¹,

Bonnefoy²,

Ducrozet³

et al. 2020

Phys. Rev. Fluids

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We study experimentally the early stages of integrable turbulence of unidirectional deep water gravity waves. By generating partially coherent waves in a 148 m long wave flume, we observe the emergence of high-amplitude structures formed by nonlinear focusing, commonly referred to as rogue waves. This work confronts the experiment with two recent results obtained in the framework of the nonlinear Schrödinger equation (NLSE), namely that (i) these structures can be locally fitted by a Peregrine soliton and (ii) their emergence leaves a visible trace on the evolution of statistical parameters such as kurtosis. Although Peregrine solitons have been observed for almost ten years in experiments using a deterministic forcing, we report their first systematic study in hydrodynamics with a random forcing. We show that (i) yields accurate results as long as the wave steepness remains moderate, whereas (ii) is very robust and remains valid beyond the assumption of integrability. Numerical simulations of the NLSE and of the fully nonlinear dynamical equations are also performed to support these results.

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Section: Discussionsupporting

confidence: 83%

Section: Introductionmentioning

confidence: 82%

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

Emergence of Peregrine solitons in integrable turbulence of deep water gravity waves

Michel¹,

Bonnefoy²,

Ducrozet³

et al. 2020

Phys. Rev. Fluids

Self Cite

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“…By scale invariance of the NLSE, such a regime can be attained whenever a peak is large and focused enough that the nonlinear term dominates over dispersion. In fiber optics [47,48], emerging Peregrine-like structures have been observed out of a random background. For the highly nonlinear case, in Fig.…”

Section: B Nonlinear Regime and Peregrine Solitonsmentioning

confidence: 99%

Experimental Evidence of Hydrodynamic Instantons: The Universal Route to Rogue Waves

et al. 2019

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A statistical theory of rogue waves is proposed and tested against experimental data collected in a long water tank where random waves with different degrees of nonlinearity are mechanically generated and free to propagate along the flume. Strong evidence is given that the rogue waves observed in the tank are hydrodynamic instantons, that is, saddle point configurations of the action associated with the stochastic model of the wave system. As shown here, these hydrodynamic instantons are complex spatio-temporal wave field configurations, which can be defined using the mathematical framework of Large Deviation Theory and calculated via tailored numerical methods. These results indicate that the instantons describe equally well rogue waves that originate from a simple linear superposition mechanism (in weakly nonlinear conditions) or from a nonlinear focusing one (in strongly nonlinear conditions), paving the way for the development of a unified explanation to rogue wave formation.

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“…By scale invariance of the NLSE, such a regime can be attained whenever an initial condition is characterized by large enough wave groups for which the nonlinear term dominates over the dispersive one. In fiber optics [53,54], emerging Peregrine-like structures have been observed out of a random background. For the highly nonlinear case, in Fig.…”

Section: B Nonlinear Regime and Peregrine Solitonsmentioning

confidence: 99%

A Unifying Framework for Describing Rogue Waves

Trillo

Chabchoub

2019

Physics

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A statistical theory of rogue waves is proposed and tested against experimental data collected in a long water tank where random waves with different degrees of nonlinearity are mechanically generated and free to propagate along the flume. Strong evidence is given that the rogue waves observed in the tank are hydrodynamic instantons, that is, saddle point configurations of the action associated with the stochastic model of the wave system. As shown here, these hydrodynamic instantons are complex spatiotemporal wave field configurations which can be defined using the mathematical framework of large deviation theory and calculated via tailored numerical methods. These results indicate that the instantons describe equally well rogue waves created by simple linear superposition (in weakly nonlinear conditions) or by nonlinear focusing (in strongly nonlinear conditions), paving the way for the development of a unified explanation to rogue wave formation.

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Effect of local Peregrine soliton emergence on statistics of random waves in the one-dimensional focusing nonlinear Schrödinger equation

Cited by 27 publications

References 55 publications

Emergence of Peregrine solitons in integrable turbulence of deep water gravity waves

Emergence of Peregrine solitons in integrable turbulence of deep water gravity waves

Experimental Evidence of Hydrodynamic Instantons: The Universal Route to Rogue Waves

A Unifying Framework for Describing Rogue Waves

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