Cubic–quartic solitons for twin-core couplers in optical metamaterials

Zayed, Elsayed M.E.; Gepreel, Khaled A.; Biswas, Anjan; Dakova, A.; Ekici, Mehmet; Alshehri, Hashim M.; Belić, Milivoj R.

doi:10.1016/j.ijleo.2021.167632

Cited by 10 publications

(6 citation statements)

References 44 publications

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“…Zi Liang-Li [12] proposed a generalized version of sub-ODE method, while Zayed and Alngar [13] introduced the modified Sub-ODE method, Recently, Zayed et al [14] have suggested the addendum to modified sub-ODE method which will be applied here to solve Eq. ( 5).…”

Section: Enhanced Sub-ode Approachmentioning

confidence: 99%

“…It is well known [12][13][14] that Eq. ( 8) has many particular solutions which will be used throughout this section to find the optical soliton solutions of Eq.…”

Section: Enhanced Sub-ode Approachmentioning

confidence: 99%

“…This is an unique and novel concept of conjoining three pre-existing nonlinear evolution equations that govern the propagation of solitons through optical fibers into a single equation [6][7][8][9][10]. This is the combination of the nonlinear Schrödinger's equation (NLSE), Lakshmanan-Porsezian-Daniel (LPD) model and the Sasa-Satsuma equation [11][12][13][14][15]. Subsequently during the same year, a different form of concatenation model, with dispersive components included, gave way to the dispersive concatenation model [16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

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Optical solitons for dispersive concatenation model with power-law of self-phase modulation: a sub-ODE approach

Zayed,

Gepreel,

El-Horbaty

et al. 2024

J Opt

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This work retrieves a plethora of optical soliton solutions to the dispersive concatenation model with power-law of self-phase modulation. The implementation of the sub-ODE method and its variations and versions yielded such soliton solutions. The intermediary functions were Weierstrass’ elliptic functions as well as Jacobi’s elliptic functions. Their special cases gave way to soliton solutions. In particular, for Jacobi’s elliptic functions, when the modulus of ellipticity approached unity, the soliton solutions have naturally emerged.

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Section: Enhanced Sub-ode Approachmentioning

confidence: 99%

“…It is well known [12][13][14] that Eq. ( 8) has many particular solutions which will be used throughout this section to find the optical soliton solutions of Eq.…”

Section: Enhanced Sub-ode Approachmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Optical solitons for dispersive concatenation model with power-law of self-phase modulation: a sub-ODE approach

Zayed,

Gepreel,

El-Horbaty

et al. 2024

J Opt

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“…In the spirit of [30,31], it needs to demonstrate the goodness of fit performance of the new copulas using real data analysis; • Beyond probability and statistics, one can think of applying the proposed copulas in mathematical physics, as in the topics considered in [36][37][38]; • In view of the established theory, one can also think of constructing a new measure of correlation that fully takes into account the oscillating nature of the multivariate trigonometric copulas, following the ideas developed in [32].…”

Section: Concluding Remarks and Perspectivesmentioning

confidence: 99%

On New Types of Multivariate Trigonometric Copulas

Chesneau

2021

AppliedMath

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Copulas are useful functions for modeling multivariate distributions through their univariate marginal distributions and dependence structures. They have a wide range of applications in all fields of science that deal with multivariate data. While there is a plethora of copulas, those based on trigonometric functions, especially in dimensions greater than two, have received much less attention. They are, however, of interest because of the properties of oscillation and periodicity of the trigonometric functions, which can appear in certain models of correlation of natural phenomena. In order to fill this gap, this paper introduces and investigates two new types of “multivariate trigonometric copulas”. Their main theoretical properties are studied, and some perspectives for applications are sketched for future work. In particular, we show that the proposed copulas are symmetric, not associative, with no orthant dependence, and with copula densities that have wide oscillations, which remains an uncommon property in the field. The expressions of their multivariate Spearman’s rho are also determined. Furthermore, the first type of the proposed copulas has the interesting feature of having a multivariate Spearman’s rho equal to 0 for all of the dimensions. Some graphic evidence supports the findings. Some mathematical formulas involving the product of n trigonometric functions may be of independent interest.

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“…One of the most popular technologies employed in the research studies is based on adding another form of dispersion such as Bragg gratings dispersion, pure-cubic dispersion, pure-quartic dispersion, cubic-quartic dispersion and many others. 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].…”

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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Cubic–quartic solitons for twin-core couplers in optical metamaterials

Cited by 10 publications

References 44 publications

Optical solitons for dispersive concatenation model with power-law of self-phase modulation: a sub-ODE approach

Optical solitons for dispersive concatenation model with power-law of self-phase modulation: a sub-ODE approach

On New Types of Multivariate Trigonometric Copulas

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

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