Cubic–quartic optical soliton perturbation with Fokas–Lenells equation by sine–Gordon equation approach

Yıldırım, Yakup; Biswas, Anjan; Dakova, A.; Khan, Salam; Moshokoa, Seithuti P.; Alzahrani, Abdullah Khamis; Belić, Milivoj R.

doi:10.1016/j.rinp.2021.104409

Cited by 16 publications

(6 citation statements)

References 24 publications

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“…Self-phase modulation (SPM) is one of the way to regularize this unbalanced transmission. However, where CD is low, the cubic and quartic nonlinearity terms are added to model and control this balance [21]. When the CD term is omitted and the third-order dispersion (3OD) and fourth-order dispersion (4OD) terms are added, the resulting model is the cubic-quartic Fokas-Lenells equation (CQFLE) [22]:…”

Section: Introductionmentioning

confidence: 99%

RETRACTED ARTICLE: Obtaining optical soliton solutions of the cubic–quartic Fokas–Lenells equation via three different analytical methods

et al. 2022

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In this study, we have focused on finding soliton solutions of the cubic-quartic Fokas-Lenells equation, which models the nonlinear pulse transmission through optical fiber, is a pretty new and updated model. We have used three different efficient analytical methods, namely, the Sinh-Gordon expansion method, enhanced modified extended tanh expansion method and unified Riccati equation expansion method. By modifying our proposed method and using it effectively, we have obtained much more optical solutions. We have supported the results with the 3D surface, 2D and contour plots of the soliton solutions, such as singular, periodic, periodic-singular, dark and M-shaped solitons. The originality of the method we propose is that it has never been used before. With the innovation of the method, we have obtained M-shaped solitons, which are very rarely obtainable in soliton waves. On the other hand, enhanced modified extended tanh expansion method have provided us more extra solutions. As the last and most important part, in order to examine physical behaviors, we have investigated the effect of the coefficient of the fourth order dispersion parameter on wave propagation by presenting the graphical representation.

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Section: Introductionmentioning

confidence: 99%

RETRACTED ARTICLE: Obtaining optical soliton solutions of the cubic–quartic Fokas–Lenells equation via three different analytical methods

et al. 2022

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“…All derived solutions are entirely new and different than the ones found in the literatures. Comparing the results obtained here with the corresponding results extracted in the previous studies, it is found that all solutions retrieved in [27] by using the sine-Gordon equation integration scheme can be deduced in this work when B = 0. The created traveling wave solutions include various wave structures such as bright soliton, combo dark-bright soliton, singular soliton, combo singular soliton and periodic waves.…”

Section: Resultssupporting

confidence: 78%

“…For example, the combination of fourth-order dispersion (4OD) and third-order dispersion (3OD) terms can completely compensate for low CD and gives rise to creation of the so-called cubic-quartic (CQ) solitons, see the references [19][20][21][22][23][24]. Later, the model of FLE is developed to include 4OD and 3OD terms and that means CQ solitons can be constructed in polarization preserving fibers [25][26][27]. The current study mainly discusses CQ-FLE with perturbation terms of Hamiltonian type.…”

Section: Introductionmentioning

confidence: 99%

Cubic–quartic optical soliton perturbation and modulation instability analysis in polarization-controlled fibers for Fokas–Lenells equation

Al-Ghafri¹,

Krishnan²,

Biswas³

2022

J. Eur. Opt. Society-Rapid Publ.

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The objective of this study is to investigate miscellaneous wave structures for perturbed Fokas–Lenells equation (FLE) with cubic-quartic dispersion in polarization-preserving fibers. Based on the improved projective Riccati equations method, various types of soliton solutions such as bright soliton, combo dark–bright soliton, singular soliton and combo singular soliton are constructed. Additionally, a set of periodic singular waves are also retrieved. The dynamical behaviors of some obtained solutions are depicted to provide a key to understanding the physics of the model. The modulation instability of the FLE is reported by employing the linear stability analysis which shows that all solutions are stable.

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“…Here, α 1 , α 2 , b, µ, p, q and β are real constants. Recently, pFL equation has been studied for some researchers using improved Adomian decomposition algorithm [30], modified extended tanh function scheme [29], sine-Gordon equation approach [31], complex envelope ansatz method [32], Kudryashov methods [33,34], Riccati-Bernoulli Sub-ODE method [35], exp(-φ(ξ))-expansion method [36], semi-inverse variational principle [37], G − G ′ expansion and Jacobi's elliptic function method [38]. In this article, we aim to extract abundant soliton solutions in the explicit form for the pFL equation using Sardar sub-equation method and to determine constrain conditions for the existence of the solutions.…”

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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Cubic–quartic optical soliton perturbation with Fokas–Lenells equation by sine–Gordon equation approach

Cited by 16 publications

References 24 publications

RETRACTED ARTICLE: Obtaining optical soliton solutions of the cubic–quartic Fokas–Lenells equation via three different analytical methods

RETRACTED ARTICLE: Obtaining optical soliton solutions of the cubic–quartic Fokas–Lenells equation via three different analytical methods

Cubic–quartic optical soliton perturbation and modulation instability analysis in polarization-controlled fibers for Fokas–Lenells equation

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

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