New general extended direct algebraic approach for optical solitons of Biswas-Arshed equation through birefringent fibers

Munawar, Maham; Jhangeer, Adil; Pervaiz, A.; Ibraheem, Farheen

doi:10.1016/j.ijleo.2020.165790

Cited by 38 publications

(11 citation statements)

References 41 publications

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“…The whole portion provides a concise but thorough overview as well as implementation of the present approach [32][33][34]. We analyze the nonlinear fractional PDEs listed below:…”

Section: Implementation Of the Extended Direct Algebraic Methodsmentioning

confidence: 99%

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Analytical Analyses for a Fractional Low-Pass Electrical Transmission Line Model with Dynamic Transition

2022

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This research explores the solitary wave solutions, including dynamic transitions for a fractional low-pass electrical transmission (LPET) line model. The fractional-order (FO) LPET line mathematical system has yet to be published, and neither has it been addressed via the extended direct algebraic technique. A computer program is utilized to validate all of the incoming solutions. To illustrate the dynamical pattern of a few obtained solutions indicating trigonometric, merged hyperbolic, but also rational soliton solutions, dark soliton solutions, the representatives of the semi-bright soliton solutions, dark singular, singular solitons of Type 1 and 2, and their 2D and 3D trajectories are presented by choosing appropriate values of the solutions’ unrestricted parameters. The effects of fractionality and unrestricted parameters on the dynamical performance of achieved soliton solutions are depicted visually and thoroughly explored. We furthermore discuss the sensitivity assessment. We, however, still examine how our model’s perturbed dynamical framework exhibits quasi periodic-chaotic characteristics. Our investigated solutions are compared with those listed in published literature. This research demonstrates the approach’s profitability and effectiveness in extracting a range of wave solutions to nonlinear evolution problems in mathematics, technology, and science.

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“…The whole portion provides a concise but thorough overview as well as implementation of the present approach [32][33][34]. We analyze the nonlinear fractional PDEs listed below:…”

Section: Implementation Of the Extended Direct Algebraic Methodsmentioning

confidence: 99%

“…Nonlinear differential equations can be solved using a variety of strategies. The new extended direct algebraic technique provides such illustration [32][33][34].…”

Section: Introductionmentioning

confidence: 99%

Analytical Analyses for a Fractional Low-Pass Electrical Transmission Line Model with Dynamic Transition

2022

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“…A brief but comprehensive background of the existing approach, the extended direct algebraic technique [51][52][53][54], is provided in the whole portion. Since the extended algebraic method is new and more general as it contains different class of functions such as dark soliton solutions, the family of semi-bright soliton outcomes, dark singular soliton outcomes, singular outcomes of soliton of Type 1 and 2, soliton outcomes involving trigonometric function, mixed hyperbolic function, and rational functions.…”

Section: Overview Of the Extended Direct Algebraic Methodsmentioning

confidence: 99%

Analysis of electron acoustic waves interaction in the presence of homogeneous unmagnetized collision-free plasma

Jhangeer

Munawar²,

Atangana

et al. 2021

Phys. Scr.

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In this research, the transmission and interaction of nonlinear electron acoustic waves (EAWs) in such an unmagnetized, homogeneous, collision-free plasma composed of hot and cold electrons together with stationary ions throughout in the background have been analyzed. For the small-amplitude limit, the Korteweg–de Vries (KdV) equation for (EAWs) have been extracted. For electron acoustic solitary waves (EASWs), using the new extended direct algebraic approach, soliton solutions have also documented. The parametric analysis demonstrated that the hot to cold electron ratio and hot electron superthermal play a key role in changing the (EASWs) amplitude. The family of semi-bright solitons, dark singular solitons, Type 1 as well as 2 single solitons, trigonometric, intermingled hyperbolic and rational solitons was constructed and tested with the assistance of the innovative package software of numerical computations. The results show that the method is clear and efficient, produces analytical results in a generalized form, and these findings can also help resolve the difficulties and predicaments in the relevant disciplines of plasma physics and may be useful for studying the relationship between two (EASWs) in astrophysical and laboratory plasma. The solutions presented in this prototype are the latest in a literature review. For physical interpretation, some randomly selected solutions are shown graphically. Conclusions are held at the end.

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“…In literature, many powerful methods are available for solving analytically the NLPDEs. For example; the unified algebraic method [9], F-expansion method [10,11], sine-Gordon method [12,13], extended rational sin-cos/sinhcosh method [14], new general extended direct algebraic method [15]. Besides, to get more abundant solutions, the researchers try to introduce new methods or modify or extend the existing methods such as modified extended tanh-function method [16,17], new Kudryashov method, [18] , extended, modified auxiliary equation method [19,20].…”

Section: Introductionmentioning

confidence: 99%

Derivation of optical solitons of dimensionless Fokas-Lenells equation with perturbation term using Sardar sub-equation method

Çinar

Seçer

Özişik

et al. 2022

Preprint

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This paper presents investigation of soliton solutions for the perturbed Fokas-Lenells (pFL) equation, has a vital role in optics, using Sardar sub-equation method. The equation models the propagation in ultrashort light pulses in optical fibers. Using appropriate wave transformation, the pFL equation is reduced to a nonlinear ordinary differential equation (NLODE). The solutions of this NLODE equation are assumed to be in the suggested form by the Sardar sub-equation method. Hence, an algebraic equation system is obtained by substituting the trial solutions and their necessary derivatives into the NLODE. After finding the unknowns in the system, the soliton solutions of the perturbed Fokas-Lenells equation are extracted. The method produces various kinds of solitons such as the dark, singular and periodic. To show physical representations of the solitons, 2D, 3D and contour plots of the solutions are demonstrated via computer algebraic systems. It is expected that derived solutions may be useful for future works in various fields of science, especially optics and so, it may contribute to optic fiber industry.

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New general extended direct algebraic approach for optical solitons of Biswas-Arshed equation through birefringent fibers

Cited by 38 publications

References 41 publications

Analytical Analyses for a Fractional Low-Pass Electrical Transmission Line Model with Dynamic Transition

Analytical Analyses for a Fractional Low-Pass Electrical Transmission Line Model with Dynamic Transition

Analysis of electron acoustic waves interaction in the presence of homogeneous unmagnetized collision-free plasma

Derivation of optical solitons of dimensionless Fokas-Lenells equation with perturbation term using Sardar sub-equation method

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