Localized structures and spatiotemporal chaos: comparison between the driven damped sine-Gordon and the Lugiato-Lefever model

Ferré, Michel; Clerc, Marcel G.; Coulibally, Saliya; Rojas, R. G.; Tlidi, Mustapha

doi:10.1140/epjd/e2017-80072-3

Cited by 27 publications

(21 citation statements)

References 57 publications

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“…The Lugiato-Lefever equation was used to investigate analytically the nature, stability and bifurcation behaviour of these patterns that could be localized or extended, stationary or nonstationary, and in the latter case, periodic or aperiodic. Interestingly, it has to be emphasized that the dynamical properties of the LLE are still under investigation from a purely mathematical point of view [28][29][30][31], and are continuously providing new insights with regards to the relationship between the LLE and other nonlinear PDEs [32]. Beyond the theoretical analysis, the dissipative patterns of WGM resonators are also enabling technology in several areas of photonics technology that would benefit from a better understanding of their properties [9,10,[12][13][14][33][34][35][36].…”

Section: Resultsmentioning

confidence: 99%

A taxonomy of optical dissipative structures in whispering-gallery mode resonators with Kerr nonlinearity

Balakireva

Chembo

2018

Phil. Trans. R. Soc. A.

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In this paper, the research related to the formation of optical dissipative structures in Kerr-nonlinear whispering-gallery mode resonators pumped with continuous-wave lasers is reviewed. Pattern formation in these systems can be analysed using the paradigmatic Lugiato-Lefever model, which is a partial differential equation ruling the dynamics of the intra-cavity laser field. Various dissipative structures such as Turing rolls, solitons, breathers and spatio-temporal chaos can emerge in the resonator depending on the laser power and frequency. The bifurcation analysis enables a classification of these patterns, and also permits identification of their basins of attraction.This article is part of the theme issue 'Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 1)'.

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Section: Resultsmentioning

confidence: 99%

A taxonomy of optical dissipative structures in whispering-gallery mode resonators with Kerr nonlinearity

Balakireva

Chembo

2018

Phil. Trans. R. Soc. A.

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“…The LLE is widely used in the setting of nonlinear optics, and can also be derived in the small amplitude limit from the ACdriven damped sine-Gordon equation [34,35]. As such the LLE can describe a variety of systems, including coupled pendula, extended Josephson junctions, easy-axis ferromagnets in microwave fields, rf-driven plasmas, whispering gallery mode resonators, and chemical reaction-diffusion systems (see, e.g., Refs.…”

Section: A Relation To Lugiato-lefever Modelmentioning

confidence: 99%

“…[35,36] and references therein). Our system corresponds to the case of anomalous dispersion α < 0, defocussing nonlinearity β > 0, and blue-detuned driving Ω > 0; however, all of these may in general be of either sign [35] depending on the physical system. The LLE and generalized versions also arise in the context of superfluid excitonpolariton systems with coherent pumping [28,[37][38][39][40][41][42].…”

Section: A Relation To Lugiato-lefever Modelmentioning

confidence: 99%

Bistability and nonequilibrium condensation in a driven-dissipative Josephson array: a c-field model

Reeves

2021

Preprint

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Developing theoretical models for nonequilibrium quantum systems poses significant challenges. Here we develop and study a multimode model of a driven-dissipative Josephson junction chain of atomic Bose-Einstein condensates, as realised in the experiment of Labouvie et al.[Phys. Rev. Lett. 116, 235302 (2016)]. The model is based on c-field theory, a beyond-mean-field approach to Bose-Einstein condensates that incorporates fluctuations due to finite temperature and dissipation. We find the c-field model is capable of capturing all key features of the nonequilibrium phase diagram, including bistability and a critical slowing down in the lower branch of the bistable region. Our model is closely related to the so-called Lugiato-Lefever equation, and thus establishes new connections between nonequilibrium dynamics of ultracold atoms with nonlinear optics, exciton-polariton superfluids, and driven damped sine-Gordon systems.

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“…For example, let us consider here the continuum limit of a chain of pendulums coupled through elastic restoring force and damped friction, governed by the damped driven sine-Gordon equations [24][25][26] (2)-( 5) with a Gaussian white noise ǫ(x, t) in case of the standard deviation of σ n = 0, σ n = 10 −18 and σ n = 10 −20 , respectively. Using the reproducible/reliable result in case of σ n = 0 as the benchmark solution, we can accurately investigate the influence of the tiny environmental noises in cases of σ n = 10 −18 and σ n = 10 −20 , respectively.…”

Section: Some Illustrative Ultra-chaosmentioning

confidence: 99%

Ultra-chaos: an insurmountable objective obstacle of reproducibility and replicability

Liao

Qin²

2021

Preprint

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It is crucial for scientific progress to be able to replicate scientific findings [1-4], because scientific claims should gain credence due to the reproducibility and replicability of their main supporting evidences. However, according to Nature’s survey of 1,576 researchers, more than 70% of the surveyed failed to reproduce another scientist’s experiments, and more than half agreed that there exists a significant “crisis of reproducibility” [2]. Here we reveal a new classification of chaos: normal-chaos and ultra-chaos. Unlike a normal-chaos, statistics of an ultra-chaos are sensitive to small disturbances. Some illustrative examples of ultra-chaos are given here. It is found that statistical non-reproducibility is indeed an inherent property of an ultra-chaos that is at a higher-level of disorder than a normal-chaos. It is impossible in practice to replicate experimental/numerical results of an ultra-chaos even in statistical meanings, since random environmental noises always exist and are out of control. Thus, ultra-chaos is indeed an insurmountable objective obstacle of reproducibility and replicability. Similar to Goedel’s incompleteness theorem, such kind of “incompleteness of reproducibility” reveals a limitation of scientific researches. It opens a new door and possibility to study reproducibility crisis, statistical significance, computational fluid dynamics (CFD), chaos theory, turbulence theory, and so on.

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Localized structures and spatiotemporal chaos: comparison between the driven damped sine-Gordon and the Lugiato-Lefever model

Cited by 27 publications

References 57 publications

A taxonomy of optical dissipative structures in whispering-gallery mode resonators with Kerr nonlinearity

A taxonomy of optical dissipative structures in whispering-gallery mode resonators with Kerr nonlinearity

Bistability and nonequilibrium condensation in a driven-dissipative Josephson array: a c-field model

Ultra-chaos: an insurmountable objective obstacle of reproducibility and replicability

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