Random Generation of Coherent Solitary Waves from Incoherent Waves

Wu, Mingzhong; Krivošı́k, Pavol; Kalinikos, B. A.; Patton, Carl E.

doi:10.1103/physrevlett.96.227202

Cited by 35 publications

(18 citation statements)

References 20 publications

(27 reference statements)

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“…Over the past two decades yttrium-iron-garnet (Y 3 Fe 5 O 12 , YIG) magnetic thin films have been fruitfully studied by numerous experimental groups and have demonstrated a rich variety of nonlinear phenomena. These include bright and dark envelope solitons [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24], soliton trains [25,26], möbius solitons [27], Fermi-Pasta-Ulam and spatial recurrence [28,29], soliton fractals [30], random solitons [31], chaotic spin waves [32][33][34], multiple solitons [35] and chaotic solitons [36,37].…”

Section: Introductionmentioning

confidence: 99%

Complex solitary wave dynamics, pattern formation and chaos in the gain–loss nonlinear Schrödinger equation

Anderson

Ryan

et al. 2014

New J. Phys.

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A numerical exploration of a gain-loss nonlinear Schrödinger equation was carried out utilizing over 180 000 core hours to conduct more than 10 000 unique simulations in an effort to characterize the model's six dimensional parameter space. The study treated the problem in full generality, spanning a minimum of eight orders of magnitude for each of three linear and nonlinear gain terms and five orders of magnitude for higher order nonlinearities. The gain-loss nonlinear Schrödinger equation is of interest as a model for spin wave envelopes in magnetic thin film active feedback rings and analogous driven damped nonlinear physical systems. Bright soliton trains were spontaneously driven out of equilibrium and behaviors stable for tens of thousands of round trip times were numerically identified. Nine distinct complex dynamical behaviors with lifetimes on the order of ms were isolated as part of six identified solution classes. Numerically located dynamical behaviors include: (i) low dimensional chaotic modulations of bright soliton trains; (ii) spatially symmetric/asymmetric interactions of solitary wave peaks; (iii) dynamical pattern formation and recurrence; (iv) steady state solutions; and

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Section: Introductionmentioning

confidence: 99%

Complex solitary wave dynamics, pattern formation and chaos in the gain–loss nonlinear Schrödinger equation

Anderson

Ryan

et al. 2014

New J. Phys.

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“…Spin waves exhibit most of the properties inherent to waves of other origins, including the excitation and propagation 21,22,23 , reflection and refraction 24,25,26,27,28,29 , interference and diffraction 30,31,32,33,34,35 , focusing and self-focusing 36,37,38,39,40,41 , tunnelling 42,43 , Doppler effect 44,45,46 , and formation of spin-wave envelope solitons 47,48,49,50 . Spin-wave quantization due to the finite size effect was discovered in thin films 51,52 and more recently in laterally confined magnetic structures 53,54,55,56,57,58 , with their effect upon the high frequency permeability and the observation of a negative permeability discussed in Refs.…”

Section: Spin Waves and Effectively Continuous Magnonic Metamaterialsmentioning

confidence: 99%

Magnonic Metamaterials

Kruglyak¹,

Dvornik²,

Mikhaylovskiy³

et al. 2012

Metamaterial

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“…Let us show that the Vlasov-Langmuir-like kinetic Eq. (19) or (22) also conserves S. This is obvious for (19) since the dispersion relation (20) for κ…”

Section: Generalization For Non-stationary Statistics and Non-instantmentioning

confidence: 93%

“…The main motive for this renewal of interest is essentially due to the first experimental demonstration of incoherent solitons in photorefractive crystals [2,3]. The incoherent soliton consists of a phenomenon of self-trapping of incoherent light in a medium characterized by a noninstantaneous [4][5][6][7][8][9][10][11][12][13][14][15] or instantaneous [16][17][18][19][20][21][22][23] nonlinear response. The remarkable simplicity of experiments performed in photorefractive media has allowed for a fruitful investigation of the dynamics of incoherent nonlinear waves [11], as witnessed by several important achievements, such as, e.g., the modulational instability of incoherent optical waves [12,13,23].…”

Section: Introductionmentioning

confidence: 99%

Kinetic Description of Random Optical Waves and Anomalous Thermalization of a Nearly Integrable Wave System

et al. 2010

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International audienceThis article is composed of two parts. The first part is aimed at providing an overview on the kinetic description of random nonlinear waves considering the one-dimensional nonlinear Schrödinger (NLS) equation as a representative model of optical wave propagation. We expose, in particular, the key problem of achieving a closure of the infinite hierarchy of moment equations for the random field. The hierarchy is closed at the first order when the statistics of the random wave is non-stationary or when the response time of the nonlinearity is non-instantaneous, which, respectively, leads to the Vlasov kinetic equation and the weak-Langmuir turbulence equation. When the amount of non-stationary statistics is comparable to the amount of non-instantaneous nonlinearity, we derive a generalized Vlasov-Langmuir equation that provides a unified formulation of the Vlasov and Langmuir approaches. On the other hand, when the statistics of the random wave is stationary and the nonlinear response instantaneous, the closure of the hierarchy of moment equations requires a second-order perturbation expansion procedure, which leads to the Hasselmann (or wave turbulence) kinetic equation. Contrarily to the Vlasov and Langmuir equations, the Hasselmann equation is irreversible, a feature which is expressed by a H-theorem of entropy growth that describes wave thermalization toward the thermodynamic equilibrium distribution, i.e. the Rayleigh-Jeans (RJ) spectrum. In the second part of the paper, we discuss a process of anomalous thermalization by considering the example of the scalar NLS equation whose integrability is broken by the presence of third-order dispersion. The anomalous thermalization is characterized by an irreversible evolution of the wave toward an equilibrium state of a fundamental different nature than the conventional RJ equilibrium state. The wave turbulence kinetic equation reveals that the anomalous thermalization is due to the existence of a local invariant in frequency space J ω, which originates in degenerate resonances of the system. In contrast to integral invariants that lead to a generalized RJ distribution, here, it is the local nature of the invariant J ω that makes the new equilibrium states fundamentally different than the usual RJ equilibrium states. We study in detail the anomalous thermalization by means of numerical simulations of the NLS equation and of the wave turbulence equation by using an improved criterion of applicability of the kinetic theory. The spectrum of the field is shown to exhibit an intriguing asymmetric deformation, which is characterized by the unexpected emergence of a constant spectral pedestal in the long-term evolution of the field. It turns out that the local invariant J ω explains all the essential properties of the anomalous thermalization of the wave

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Random Generation of Coherent Solitary Waves from Incoherent Waves

Cited by 35 publications

References 20 publications

Complex solitary wave dynamics, pattern formation and chaos in the gain–loss nonlinear Schrödinger equation

Complex solitary wave dynamics, pattern formation and chaos in the gain–loss nonlinear Schrödinger equation

Magnonic Metamaterials

Kinetic Description of Random Optical Waves and Anomalous Thermalization of a Nearly Integrable Wave System

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