Controllable soliton propagation of Airy-Gaussian beams under the fractional effect

Yan, Xiaona; Wang, Pengxiang; Zhang, Jing; Guo, Teng; Gao, Ru; Ren, Shumin

doi:10.1016/j.ijleo.2021.167431

Cited by 7 publications

(7 citation statements)

References 26 publications

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“…The physical parameters to assess the presence and the dynamics of solitons are manifold. They include surface elevation, wave height, phase velocity (i.e., the rate at which the wave phase propagates), wavelength, spatiotemporal evolution of the normalized force as a function of a fixed or infinite horizontal distance, breathing period and maximum intensity, trajectories, velocities, acceleration, medium depth, material parameters [2,45]. In fluid media like seas or channels, also surface tension, density, gravity, channel height, water depth, carrier frequency and amplitude of the background wave [44] conspire to generate the solitons' features.…”

Section: The Remarkable Physical Features Of Solitonsmentioning

confidence: 99%

Approaching Electroencephalographic Pathological Spikes in Terms of Solitons

Tozzi

2024

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A delicate balance between dissipative and nonlinear forces allows traveling waves termed solitons to preserve their shape and energy for long distances without steepening and flattening out. Solitons are so widespread that they can generate both destructive waves on oceans’ surfaces and noise-free message propagation in silica optic fibers. They are naturally observed or artificially produced in countless physical systems at very different coarse-grained scales, from solar winds to Bose–Einstein condensates. We hypothesize that some of the electric oscillations detectable by scalp electroencephalography (EEG) could be assessed in terms of solitons. A nervous spike must fulfill strict mathematical and physical requirements to be termed a soliton. They include the proper physical parameters like wave height, horizontal distance and unchanging shape; the appropriate nonlinear wave equations’ solutions and the correct superposition between sinusoidal and non-sinusoidal waves. After a thorough analytical comparison with the EEG traces available in the literature, we argue that solitons bear striking similarities with the electric activity recorded from medical conditions like epilepsies and encephalopathies. Emerging from the noisy background of the normal electric activity, high-amplitude, low-frequency EEG soliton-like pathological waves with relatively uniform morphology and duration can be observed, characterized by repeated, stereotyped patterns propagating on the hemispheric surface of the brain over relatively large distances. Apart from the implications for the study of cognitive activities in the healthy brain, the theoretical possibility to treat pathological brain oscillations in terms of solitons has powerful operational implications, suggesting new therapeutical options to counteract their detrimental effects.

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Section: The Remarkable Physical Features Of Solitonsmentioning

confidence: 99%

Approaching Electroencephalographic Pathological Spikes in Terms of Solitons

Tozzi

2024

Signals

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“…( 3) for integral calculation, the analytical solution of Eq. ( 1) corresponding to the initial beam (4) can be derived as , (7) From Eq. ( 5), one can observe that the initial state is also a cosh-Gaussian wave packet in k space.…”

Section: Theoretical Modelmentioning

confidence: 99%

“…As a helpful method, the photonic potential is extensively investigated and employed in linear and nonlinear system. It is well known that different external potentials can be achieved by appropriately adjusting the refractive index of the material and various forms of potentials have been reported recently, such as linear potential [1,2], parabolic potential [3][4][5], symmetric potential barrier [6], Gaussian potential [7], dynamic potentials [8], etc. However, among these potentials, the parabolic potential, extensively applied in laser-plasma physics [9], Bose-Einstein condensates [10], and ultracold atoms [11], is one of the most attractive and concerned potential mode.…”

Section: Introductionmentioning

confidence: 99%

Controllable transmission of chirped cosh-Gaussian beams in parabolic potential

Song

Fang

Liu

et al. 2022

Preprint

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In our study, based on the normalized linear Schrödinger equation, we have analytically and numerically investigated the propagation dynamics of chirped cosh-Gaussian beams in a medium with parabolic potential. The obtained results show that cosh-Gaussian beams perform a periodic auto-focusing behavior and the parabolic potential determines the focusing ability, including the focal distance as well as peak intensity at the focus. Especially, the intensity distributions and waveform of cosh-Gaussian beam are related to the initial parameter of cosh function. Furthermore, we also demonstrate the effect of chirp factors on the beam and find that the periodic oscillating behavior caused by linear chirp can be used to manipulated the propagation trajectory of beam, but linear chirp does not affect the focal intensity. While the quadratic chirp can enhance the focusing ability and peak intensity of beam on the axis, which indicates that the quadratic chirp factor plays a significant role in the modulation of the energy localization.

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“…solitons. In fractional nonlinear regime, a series of interesting phenomena have been reported by many investigations, such as propagation of super-Gaussian beam [31], propagation and interaction of Airy beams [32][33][34], evolution of Bessel-Gaussian beam [35], Nonlinear conical diffraction [36], and different types of optical solitons [37][38][39][40][41][42][43][44][45][46][47][48][49][50][51]. Although 1D DSs have been studied in FNLSE with defective parity-time symmetric potential [52] and Kerr nonlinearity [53], properties of 1D and 2D DSs with saturable nonlinearity in FNLSE remain to be studied in detail.…”

Section: Introductionmentioning

confidence: 99%

Defect solitons supported by optical lattice with saturable nonlinearity in fractional Schrödinger equation

Wang

Xia²,

Chen

et al. 2023

Phys. Scr.

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We address the existence, stability, and propagation dynamics of both one- and two-dimensional defect solitons supported by optical lattice with saturable nonlinearity in fractional Schrödinger equation. Under the influence of fractional effect, in one dimension, solitons exist stably in limited regions in the semi-infinite bandgap with high and low power both for a negative and positive defect lattice. In the first bandgap, solitons are stable for negative defect lattice, while unstable for positive defect lattice. In the second bandgap, only stable solitons can propagate in small regions for the positive defect lattice. With increasing the Lévy index from 1 to 2, the power of the defect solitons decreases in the semi-infinite bandgap and increases in the first bandgap. Linear stability analyses show that, the domains of stability for defect solitons strongly depend on the Lévy index, defect strength and different bandgaps. In two dimension, defect solitons can exist stably at high and moderate power regions in the semi-infinite bandgap and all regions in the first bandgap with negative defect lattice, while they are stable at high, moderate and low power regions in the semi-infinite bandgap and unstable in the first bandgap with positive defect lattice.

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Controllable soliton propagation of Airy-Gaussian beams under the fractional effect

Cited by 7 publications

References 26 publications

Approaching Electroencephalographic Pathological Spikes in Terms of Solitons

Approaching Electroencephalographic Pathological Spikes in Terms of Solitons

Controllable transmission of chirped cosh-Gaussian beams in parabolic potential

Defect solitons supported by optical lattice with saturable nonlinearity in fractional Schrödinger equation

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