Optical soliton perturbation with Chen–Lee–Liu equation

Yıldırım, Yakup; Biswas, Anjan; Asma, Mir; Ekici, Mehmet; Ntsime, Basetsana P.; Zayed, Elsayed M.E.; Moshokoa, Seithuti P.; Alzahrani, Abdullah; Belić, Milivoj R.

doi:10.1016/j.ijleo.2020.165177

Cited by 55 publications

(10 citation statements)

References 21 publications

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“… ,  and  on the right side of the equation are coefficients of nonlinear dispersion, self-steeping for short pulses and the inter-modal dispersion, respectively. In addition, the nonlinearity parameter m in the above equation defines the density for complex wave function [38].…”

Section: ( )mentioning

confidence: 99%

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Simulation and refraction event of complex hyperbolic type solitary wave in plasma and optical fiber for the perturbed Chen-Lee-Liu equation

2021

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In this presented article, modified 1/G -expansion and modified Kudryashov methods are applied to generate traveling wave solutions of perturbed Chen-Lee-Liu (CLL) equation. The similar and different aspects of the solutions produced by both analytical methods are discussed in the results and discussion section. By giving special values to the constants in the solutions obtained by analytical methods, 2D, 3D and contour graphics representing the shape of the standing wave at any time are presented. Additionally, the advantages and disadvantages of the two analytical methods are discussed and presented in the results and discussion section. Also, a solitary wave is produced by giving special values to the parameters in the hyperbolic type complex traveling wave solution. Simulations are created for different values of the frequency and velocity propagation parameters of the solitary wave. The values of these parameters are calculated for the breakage event physically. A computer package program is used for operations such as solving complex operations, drawing graphics and systems of algebraic equations.

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Section: ( )mentioning

confidence: 99%

“…When these soliton solutions are examined, special cases of these solutions are obtained, depending on the wave propagation parameter, height and density. We can classify these special cases as dark, bright and singular solitons [34]. Bright and dark solitons are related to the intensity of the wave.…”

Section: Introductionmentioning

confidence: 99%

Simulation and refraction event of complex hyperbolic type solitary wave in plasma and optical fiber for the perturbed Chen-Lee-Liu equation

2021

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“…x -W exp -expansion function procedure, [31,32], the double sub-equation method [33,34], the Jacobi elliptic function expansion method (JEFM) [35,36], the F-expansion analysis and many others [37].…”

Section: Introductionmentioning

confidence: 99%

Analytical soliton solutions for the beta fractional derivative Gross–Pitaevskii system with linear magnetic and time dependent laser interactions

Yépez-Martínez,

Inc,

Alqahtani

2024

Phys. Scr.

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The local conformable beta Atangana derivative will be considered for the introductionof the fractional Gross-Pitaevskii model with conformable derivatives of beta type. Solitonsanalytical expressions are constructed by sub-equation method with elliptical functions.New entire family of solitons were determined by considering the arising constrains over theparameters of the nonlinear fractional Gross-Pitaevskii system. The analytical expressionsfor the solitons in the fractional order case reduce to the well known solitons previouslyreported for hyperbolic and periodic tan-type singular solutions for the integer order limitvalue, when special cases of the Jacobi elliptic functions are considered. Solitons propertiesare depicted in 3-D, level and 2-D illustrations. The fractional solitons here introducedposses some interesting time evolution behavior observed in the 3-D representations, thesetime properties are not present in the integer order case and has an important dependencyon the fractional parameter of the beta derivative. The solitons here introduced for thenonlinear fractional Gross-Pitaevskii equation will be very useful in future works where additional interactions will be introduced for the study of different Bose-Einstein condensation phenomena or other nonlinear phenomena where non regular oscillations will be involved.

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“…x --expansion function method [9], the modified G 1 ( ) / ¢ -expansion and modified Kudryashov methods [15], the 6 F -expansion method [20], the Sardar sub-equation method [21], the Riccati method, the Sine-Gordon equation strategy, and the F-expansion procedure [22]. But there have been a few studies on the fractional NPCL equation.…”

Section: Introductionmentioning

confidence: 99%

Diverse optical soliton solutions of two space-time fractional nonlinear evolution equations by the extended kudryashov method

Devnath,

Akbar,

Gómez-Aguilar

2023

Phys. Scr.

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This study investigates the comprehensive optical soliton solutions to the (2+1)-dimensional nonlinear time-fractional Zoomeron equation and the space-time fractional nonlinear Chen-Lee-Liu equation using the extended Kudryashov technique. The newly defined beta derivative is used to conduct the fractional terms and investigate wide-spectral soliton solutions to the considered models. The general solutions yield a variety of typical soliton shapes, including V-shaped soliton, anti-bell-shaped soliton, kink soliton, periodic soliton, singular periodic soliton, etc. The three-dimensional, contour, and two-dimensional graphs of the derived solitons have been plotted to illustrate the structure, propagation, and influence of the fractional parameter. The precision of the acquired solutions is confirmed by reintroducing them into the original equation using Mathematica. The findings of this study indicate that the employed method has the capability of yielding compatible, creative, and useful solutions for diverse nonlinear evolution equations with fractional derivatives. This approach could introduce novel ways for unraveling other nonlinear equations and have implications in diverse sectors of nonlinear science and engineering.

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Optical soliton perturbation with Chen–Lee–Liu equation

Cited by 55 publications

References 21 publications

Simulation and refraction event of complex hyperbolic type solitary wave in plasma and optical fiber for the perturbed Chen-Lee-Liu equation

Simulation and refraction event of complex hyperbolic type solitary wave in plasma and optical fiber for the perturbed Chen-Lee-Liu equation

Analytical soliton solutions for the beta fractional derivative Gross–Pitaevskii system with linear magnetic and time dependent laser interactions

Diverse optical soliton solutions of two space-time fractional nonlinear evolution equations by the extended kudryashov method

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