Dynamical study of a time fractional nonlinear Schrödinger model in optical fibers

Shakeel, Muhammad; Bibi, Aysha; AlQahtani, Salman A.; Alawwad, Abdulaziz M.

doi:10.1007/s11082-023-05301-x

Cited by 10 publications

(4 citation statements)

References 38 publications

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“…In this section, we compare some of our most current research findings with previous published study. Shakeel et al 30 employed the exponential rational approach to explore the results of time FCNLS model involving Beta derivative. In our present work, we consider (1+1)-dimensional time FCNLS model including Beta derivative and apply the MSSE approach to obtain dark, singular, periodic and rational solutions.…”

Section: Resultsmentioning

confidence: 99%

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Analyzing the dynamical sensitivity and soliton solutions of time-fractional Schrödinger model with Beta derivative

Nadeem,

Liu,

Alsayaad

2024

Sci Rep

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In physical domains, Beta derivatives are necessary to comprehend wave propagation across various nonlinear models. In this research work, the modified Sardar sub-equation approach is employed to find the soliton solutions of (1+1)-dimensional time-fractional coupled nonlinear Schrödinger model with Beta fractional derivative. These models are fundamental in real-world applications such as control systems, processing of signals, and fiber optic networks. By using this strategy, we are able to obtain various unique optical solutions, including combo, dark, bright, periodic, singular, and rational wave solutions. In addition, We address the sensitivity analysis of the proposed model to investigate the truth that it is extremely sensitive. These studies are novel and have not been performed before in relation to the nonlinear dynamic features of these solutions. We show these behaviors in 2-D, contour 3-D structures across the associated physical characteristics. Our results demonstrate that the proposed approach offers useful results for producing solutions of nonlinear fractional models in application of mathematics and wave propagation in fiber optics.

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Section: Resultsmentioning

confidence: 99%

“…The time FCNLS model in (1+1) dimension containing a fractional derivation (FD) of beta is as follows 30 (1)…”

Section: Mathematical Modelmentioning

confidence: 99%

Analyzing the dynamical sensitivity and soliton solutions of time-fractional Schrödinger model with Beta derivative

Nadeem,

Liu,

Alsayaad

2024

Sci Rep

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“…In [30], Rafiq et al achieved period, kink, antikink, and dark solutions using the unified Riccati equation expansion method and the generalized Kudryashov method. In [31], Shakeel et al discovered various optical soliton solutions employing the generalized exponential rational function method. In the current study, we are utilizing the f + ( G ′ G ) -expansion method to find out more generalized soliton solutions.…”

Section: Resultsmentioning

confidence: 99%

“…A variety of fractional derivatives are essential to the physical phenomena of nonlinear partial differential equations, such as the Beta derivative [20], Jumarie's modified Riemann-Liouville derivative [23], the Riemann-Liouville derivative [24], the fractal derivatives [25], Atangana's conformable derivative [26], the Caputo derivative [27], and the Atangana-Baleanu fractional operator [28]. The coupled NLSE is utilized to search out the wave propagation in continuous mediums [29], which happens in the typical scenario arising slowly fluctuating waves of small amplitude, like the long-distance pulse propagation in fluid dynamics, optical fibers, nonlinear optics, quantum mechanics, and other physical nature [30,31], which reads…”

Section: Introductionmentioning

confidence: 99%

Exploring the Depths: Soliton Solutions, Chaotic Analysis, and Sensitivity Analysis in Nonlinear Optical Fibers

Shakeel,

Liu,

Alshammari

2024

Fractal Fract

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This paper discusses the time-fractional nonlinear Schrödinger model with optical soliton solutions. We employ the f+(G′G)-expansion method to attain the optical solution solutions. An important tool for explaining the particular explosion of brief pulses in optical fibers is the nonlinear Schrödinger model. It can also be utilized in a telecommunications system. The suggested method yields trigonometric solutions such as dark, bright, kink, and anti-kink-type optical soliton solutions. Mathematica 11 software creates 2D and 3D graphs for many physically important parameters. The computational method is effective and generally appropriate for solving analytical problems related to complicated nonlinear issues that have emerged in the recent history of nonlinear optics and mathematical physics. Furthermore, we venture into uncharted territory by subjecting our model to chaotic and sensitivity analysis, shedding light on its robustness and responsiveness to perturbations. The proposed technique is being applied to this model for the first time.

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A comparative study of two fractional nonlinear optical model via modified $$\left( \frac{G^{\prime }}{G^2}\right)$$-expansion method

Saboor,

Shakeel,

Liu

et al. 2023

Opt Quant Electron

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Dynamical study of a time fractional nonlinear Schrödinger model in optical fibers

Cited by 10 publications

References 38 publications

Analyzing the dynamical sensitivity and soliton solutions of time-fractional Schrödinger model with Beta derivative

Analyzing the dynamical sensitivity and soliton solutions of time-fractional Schrödinger model with Beta derivative

Exploring the Depths: Soliton Solutions, Chaotic Analysis, and Sensitivity Analysis in Nonlinear Optical Fibers

A comparative study of two fractional nonlinear optical model via modified $$\left( \frac{G^{\prime }}{G^2}\right)$$-expansion method

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