Modulational Instability in Crossing Sea States: A Possible Mechanism for the Formation of Freak Waves

Onorato, Miguel; Osborne, A. R.; Serio, M.

doi:10.1103/physrevlett.96.014503

Cited by 330 publications

(288 citation statements)

References 25 publications

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“…The asymptotic solution to the dispersion relation [Eq. (3)] that is found in the limit of large values of p leads to the saturation value of the peak gain G sat = 2π 2 2 β 2 and to the OMF f sat = √ 2 . Figure 1(c) shows that the OMF decreases monotonically to attain the asymptotic minimum value f sat as P increases (OMF/ → 1/ √ 2 = 0.707).…”

Section: Theoretical Analysis Of Polarization Modulation Instabilitymentioning

confidence: 97%

“…For instance, consider a system of coupled nonlinear Schrödinger equations (NLSEs) to describe the nonlinear interaction between wave packets in dispersive conservative media. Such coupled systems are of physical relevance in various domains such as nonlinear optics, hydrodynamics, plasma physics, multicomponent Bose-Einstein condensates, and financial systems [1][2][3][4][5]. The first multicomponent NLSE type of model with applications to physics is the well-known Manakov model [6].…”

Section: Introductionmentioning

confidence: 99%

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Polarization modulation instability in a Manakov fiber system

et al. 2015

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The Manakov model is the simplest multicomponent model of nonlinear wave theory: It describes elementary stable soliton propagation and multisoliton solutions, and it applies to nonlinear optics, hydrodynamics, and Bose-Einstein condensates. It is also of fundamental interest as an asymptotic model in the context of the widely used wavelength-division-multiplexed optical fiber transmission systems. However, although its physical relevance was confirmed by the experimental observation of Manakov (vector) solitons in a planar waveguide in 1996, there have in fact been no quantitative experiments confirming its validity for nonlinear dynamics other than soliton formation. Here, we report experiments in optical fiber that provide evidence of passband and baseband polarization modulation instabilities in a defocusing Manakov system. In the spontaneous regime, we also reveal a unique saturation effect as the pump power increases. We anticipate that such observations may impact the application of this minimal model to describe and understand more complicated phenomena in nature, such as the formation of extreme waves in multicomponent systems.

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Section: Theoretical Analysis Of Polarization Modulation Instabilitymentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Polarization modulation instability in a Manakov fiber system

et al. 2015

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“…Nowadays, it is well known that solitons collide elastically, and there are some phase shift appearing after the collision [14][15][16][17][18], which demonstrate the particle-like properties of soliton. These just provide us the knowledge about the properties of solitons before or after their collision.…”

Section: Introductionmentioning

confidence: 99%

Properties of the temporal–spatial interference pattern during soliton interaction

et al. 2015

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Interference patterns associated with soliton-soliton interaction are investigated in detail. We find that the temporal and spatial interference patterns exhibit quite different characteristics. The period of the spatial interference pattern is determined by the relative velocity of the solitons, and the temporal pattern behavior is determined by the peak amplitudes and the kinetic energy of the solitons. Analytical expressions for the periods of the interference patterns are obtained. A method for classifying the nonlinearity of many nonlinear systems is proposed. As an example, we discuss possibilities to observe these properties of solitons in a nonlinear planar waveguide.

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“…Simple nonlinear solutions of the NLS equation can serve as prototypes of freak waves in the open ocean, as shown by several theoretical works 63,64 and recent laboratory experiments 65 . A system of two coupled NLS equations were derived by Onorato et al 66 , to describe the modulational instability in the ocean. Their model can explain the occurrence of freak waves in crossing sea states.…”

Section: Discussionmentioning

confidence: 99%

Chaotic saddles in nonlinear modulational interactions in a plasma

2012

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A nonlinear model of modulational processes in the subsonic regime involving a linearly unstable wave and two linearly damped waves with different damping rates in a plasma is studied numerically. We compute the maximum Lyapunov exponent as a function of the damping rates in a two-parameter space, and identify shrimp-shaped self-similar structures in the parameter space. By varying the damping rate of the low-frequency wave, we construct bifurcation diagrams and focus on a saddle-node bifurcation and an interior crisis associated with a periodic window. We detect chaotic saddles and their stable and unstable manifolds, and demonstrate how the connection between two chaotic saddles via coupling unstable periodic orbits can result in a crisis-induced intermittency. The relevance of this work for the understanding of modulational processes observed in plasmas and fluids is discussed.

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Modulational Instability in Crossing Sea States: A Possible Mechanism for the Formation of Freak Waves

Cited by 330 publications

References 25 publications

Polarization modulation instability in a Manakov fiber system

Polarization modulation instability in a Manakov fiber system

Properties of the temporal–spatial interference pattern during soliton interaction

Chaotic saddles in nonlinear modulational interactions in a plasma

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