Dark solitons and modulational instability of the nonlinear left-handed transmission electrical line with fractional derivative order

Ahmadou, Djidere; Justin, Mibaile; Boudoue, Hubert Malwe; Betchewe, Gambo; Doka, Serge Y.; Kofané, Timoléon Crépin

doi:10.1088/1402-4896/abb5c6

Cited by 8 publications

(3 citation statements)

References 47 publications

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“…Therefore, we aim to investigate the parameters influencing the frequency of the wave. For related studies, see [37][38][39]. We begin by assuming that equation (1) is subjected to a small perturbation.…”

Section: Modulation Instabilitymentioning

confidence: 99%

Soliton solutions of time-fractional modified Korteweg-de-Vries Zakharov-Kuznetsov equation and modulation instability analysis

Onder,

Secer,

Bayram

2023

Phys. Scr.

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In this paper, we explore analytical solutions for the (3+1)-dimensional time-fractional modified Korteweg–de Vries Zakharov-Kuznetsov equation, which incorporates a conformable derivative. Our interest in this model is driven by its significant role in simulating ion-acoustic waves in magnetized plasma. We adopt the unified Riccati equation expansion method and the new Kudrashov method to discover soliton solutions. Our approach uncovers various soliton types, such as kink, singular, periodic-singular, and bright solitons. We conduct a thorough analysis of how different parameters affect wave propagation, enhancing our study with descriptive figures and insightful observations. Furthermore, we delve into the modulation instability characteristic of this model. The influence of specific parameters, like wave number and the order of the conformable derivative, on wave dynamics is demonstrated through detailed visualizations. We also present 2D and 3D graphical representations of these solutions.

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Section: Modulation Instabilitymentioning

confidence: 99%

Soliton solutions of time-fractional modified Korteweg-de-Vries Zakharov-Kuznetsov equation and modulation instability analysis

Onder,

Secer,

Bayram

2023

Phys. Scr.

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“…In 2017, Zhang et al [36] demonstrated theoretically and numerically that the Lévy index affects the fastest growing frequency and MI bandwidth and gain. Correspondingly, dark soliton [37] and bright soliton [38], instability modulations in the FSE have also been studied.…”

Section: Introductionmentioning

confidence: 99%

Periodic evolution of the Pearcey Gaussian beam under fractional effect

Ren¹,

Gao²,

Guo³

et al. 2022

J. Phys. B: At. Mol. Opt. Phys.

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In this paper, the propagation dynamics of the Pearcey Gaussian beam modeled by the fractional Schrödinger equation in linear potential have been investigated. Different from the propagation properties of the Pearcey Gaussian beam described by the standard Schrödinger equation, the diffraction-free phenomenon which is presented under the fractional Schrödinger equation with linear potential or not, is influenced by Lévy index. When the linear potential is considered, the periodic evolution of the Pearcey Gaussian beams is given, and results show that transmission period is inversely proportional to the linear potential coefficient. And the direction of beam propagation can be controlled by the symbol of linear potential parameters. The propagation of incident beam with transverse wave velocity have been studied. Moreover, the chirp does not influence the evolution period of the Pearcey Gaussian beam but the intensity distribution. These properties can be well implemented to the promising applications of Pearcey Gaussian beam in optical manipulation and optical switch.

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“…[20,21] Furthermore, considering that the all-fiber laser has the advantages of high reliability, easy operation and maintenance, and good compatibility, [22][23][24] it could be anticipated that the domain-wall soliton trains in the allfiber structure laser could greatly enhance applications in optical sensing, optical communication, and soliton multiplexed systems. [25,26] In this paper, we report the experimental observation of DW dark solitons in a ring laser with an all-fiber structure. To be more compact and compatible, the laser is mode-locked by a segment of thulium-doped fiber.…”

Section: Introductionmentioning

confidence: 99%

Generation of domain-wall solitons in an anomalous dispersion fiber ring laser*

Zhang¹,

Yang²,

Geng³

et al. 2021

Chinese Phys. B

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We report experimental observations performed using a net anomalous dispersion Er-doped fiber ring laser without polarization-selective elements, highlighting the domain-wall solitary pulses generated under the incoherent polarization coupling. By adjusting the pump power and the polarization state appropriately, bright and dark solitons can stably co-exist in the cavity, both centered at 1562.16 nm with a 3-dB spectral width of ∼ 0.15 nm and a repetition rate of 3.83 MHz. Moreover, the 0.8 mm long thulium-doped fiber (TDF) facilitated the mode-locking and self-starting of the laser. This is the first demonstration of a laser being used to generate bright and dark solitons synchronously while using TDF as the saturable absorber (SA). Except possessing the all-fiber structure, the laser exhibits good stability, which may have a significant influence on improvement of the pulse-laser design, and may broaden practical applications in optical sensing, optical communication, and soliton multiplexed systems.

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Dark solitons and modulational instability of the nonlinear left-handed transmission electrical line with fractional derivative order

Cited by 8 publications

References 47 publications

Soliton solutions of time-fractional modified Korteweg-de-Vries Zakharov-Kuznetsov equation and modulation instability analysis

Soliton solutions of time-fractional modified Korteweg-de-Vries Zakharov-Kuznetsov equation and modulation instability analysis

Periodic evolution of the Pearcey Gaussian beam under fractional effect

Generation of domain-wall solitons in an anomalous dispersion fiber ring laser*

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