Nonlinear wave collapse and strong turbulence

Robinson, P. A.

doi:10.1103/revmodphys.69.507

Cited by 391 publications

(390 citation statements)

References 309 publications

(536 reference statements)

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“…Such a blow-up behavior may result in wave collapse and optical turbulence (cf. [4], [5] and [15]). Due to the positive sign of µ j 's, the system (1.1) is of two-component self-focusing nonlinear Schrödinger equations having an increasing tendency for the solution to be trapped in regions of highest intensity.…”

Section: Introductionmentioning

confidence: 99%

Solitary and self-similar solutions of two-component system of nonlinear Schrödinger equations

Lin

Wei

2006

Physica D: Nonlinear Phenomena

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Conventionally, to learn wave collapse and optical turbulence, one must study finite-time blow-up solutions of one-component self-focusing nonlinear Schrödinger equations (NLSE). Here we consider simultaneous blow-up solutions of two-component system of self-focusing NLSE. By studying the associated self-similar solutions, we prove two components of solutions blow up at the same time. These self-similar solutions may come from solitary wave solutions with multi-bumps forming abundant geometric patterns which cannot be found in one-component self-focusing NLSE. Our results may provide the first step to investigate optical turbulence in two-component system of NLSE.

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Section: Introductionmentioning

confidence: 99%

Solitary and self-similar solutions of two-component system of nonlinear Schrödinger equations

Lin

Wei

2006

Physica D: Nonlinear Phenomena

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“…The phenomenon of turbulence appears in many areas of our experience ranging from atmospheric and oceanic rogue events, aero-and hydrodynamics, optics to cardiology and neurophysiology [1,5,[7][8][9][10][11][12][13]. Such a broad class of phenomena cannot be grasped by some single and simple model.…”

Section: Analogy Between Ds and Turbulencementioning

confidence: 97%

“…These figures demonstrate an affinity between the structures of DS and turbulence [8,23]. Both spectral structures are defined by dispersion relations: between soliton and dispersive waves for the former and Langmuir dispersion relation for the latter ( Figure 7).…”

Section: Analogy Between Ds and Turbulencementioning

confidence: 99%

“…As a consequence, a wave package decouples into a set of individual modes ("particles") which interaction can be described in the framework of kinetic theory as many-particle collisions in Bose-gas. In other words, as some degrees of freedom become very large for sufficiently large energies, phase information becomes irrelevant, and the waves decohere [8,15]. Thus, a wave can be considered as a set of decoupled "modes" n k in a spectral (or wave-number) space:…”

Section: Analogy Between Ds and Turbulencementioning

confidence: 99%

“…The turbulence in the wave-number space is defined by the Langmuir dispersion relation (parabolic black curve in the right picture). Spectral condensation at k = 0 is illustrated by shading and forms a characteristic turbulence spectrum (central red curve; right picture) with the cut-off wave-number AEk diss defined by a dissipation (adapted from [8]). destroy its internal coherence and split ("nucleate") it into a set of "internal modes" shown in Figure 6.…”

Section: Transition To a Ds Turbulencementioning

confidence: 99%

See 2 more Smart Citations

Self-Organization, Coherence and Turbulence in Laser Optics

Калашников¹,

Sorokin²

2018

Complexity in Biological and Physical Systems - Bifurcations, Solitons and Fractals

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In the last decades, rapid progress in modern nonlinear science was marked by the development of the concept of dissipative soliton (DS). This concept is highly useful in many different fields of science ranging from field theory, optics, and condensed matter physics to biology, medicine, and even sociology. This chapter aims to present a DS appearance from random fluctuations, development, and growth, the formation of the nontrivial internal structure of mature DS and its breakup, in other words, a full life cycle of DS as a self-organized object. Our extensive numerical simulations of the generalized cubicquintic nonlinear Ginzburg-Landau equation, which models, in particular, dynamics of mode-locked fiber lasers, demonstrate a close analogy between the properties of DS and the general properties of turbulent and chaotic systems. In particular, we show a disintegration of DS into a noncoherent (or partially coherent) multisoliton complex. Thus, a DS can be interpreted as a complex of nonlinearly coupled coherent "internal modes" that allows developing the kinetic and thermodynamic theory of the nonequilibrious dissipative phenomena. Also, we demonstrate an improvement of DS integrity and, as a result, its disintegration suppression due to noninstantaneous nonlinearity caused by the stimulated Raman scattering. This effect leads to an appearance of a new coherent structure, namely, a dissipative Raman soliton.

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Dynamical evidence for nonlinear Langmuir wave processes in type III solar radio bursts

Graham

Cairns

2014

JGR Space Physics

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The nonlinear processes and evolution of Langmuir waves in the source regions of type III solar radio bursts are explored in detail. Langmuir waves recorded by the Time Domain Sampler of the STEREO/WAVES instrument can be roughly classified into six groups based on the waveform, power spectra, and field strength perpendicular to the local magnetic field. It is argued that these groups correspond to either different stages of the evolution of Langmuir waves generated by electron beams or differ due to the direction of the magnetic field relative to the solar wind velocity. Approximately half of the observed Langmuir waves have strong perpendicular fields, meaning that understanding how these fields are produced is crucial for understanding type III sources. Most events recorded are either localized waveforms consistent with Langmuir eigenmodes or have two or more spectral peaks consistent with electrostatic (ES) decay of Langmuir/z mode waves. The remaining events appear to correspond to either earlier or later stages of Langmuir wave evolution or are decay events for which the Doppler shift is insufficient to distinguish the beam‐driven and product Langmuir waves. This is supported by the fact that most events exceed the threshold for ES decay even though their spectra show no evidence for decay and some of the events are observed when the solar wind flow is approximately perpendicular to the magnetic field, minimizing Doppler shifting. Low‐frequency fields produced by intense Langmuir waves are quantitatively consistent with density perturbations produced by the ponderomotive force, ion‐acoustic waves produced by ES decay, or sheath rectification. Above the observed nonlinear threshold, quantitative analysis suggests that the observed low‐frequency signals are consistent with perturbations produced by ponderomotive effects and ion‐acoustic waves produced by ES decay, but effects of sheath rectification may also contribute.

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Nonlinear wave collapse and strong turbulence

Cited by 391 publications

References 309 publications

Solitary and self-similar solutions of two-component system of nonlinear Schrödinger equations

Solitary and self-similar solutions of two-component system of nonlinear Schrödinger equations

Self-Organization, Coherence and Turbulence in Laser Optics

Dynamical evidence for nonlinear Langmuir wave processes in type III solar radio bursts

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