Solitons and conservation laws in magneto–optic waveguides having parabolic–nonlocal law of refractive index

Zayed, Elsayed M.E.; El‐Horbaty, Mahmoud; Biswas, Anjan; Kara, A. H.; Ekici, Mehmet; Asma, Mir; Alzahrani, Abdullah; Belić, Milivoj R.

doi:10.1016/j.physleta.2020.126814

Cited by 22 publications

(9 citation statements)

References 11 publications

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“…This challenge persists despite the extensive literature dedicated to constructing exact traveling wave and soliton solutions [6]- [57], [66][67][68][69][70]. In efforts to circumvent these constraints, several scholars have attempted to solve coupled equations by reducing them into single equations through the imposition of drastic constraints [58][59][60][61][62][63][64][65] (to cite just a few). However, such an approach inadvertently alters the original nature of the problem and the underlying physical phenomena these coupled equations represent.…”

Section: Introductionmentioning

confidence: 99%

“…In addition, the assumption f x y d f x y = = ( ) ( ) ( ) ( ) ( ) ( ) q x t i x t r x t i x t , exp , , , exp , (where q(x, t) is the wave function in the first line while r(x, t) is that in the second line, f(ξ), ψ(x, t) are the amplitude and the phase component of the wave respectively, and δ is a real constant), or even the less restricted one (where F(ξ) is a real valued function, and τ 0 , τ 1 , β 0 and β 1 are real constants) only allows the propagation of same types of nonlinear waves on the two lines. In this same line of action, Zayed et al [58] addressed the soliton dynamics to magneto-optic waveguides having parabolic-nonlocal law of refractive index, they made the same assumptions described above and their method only allows the propagation of the same type of waves on the two channels, excluding the possibility to have different wave propagations in both lines. In this research, we aim to address and mitigate the limitations previously identified in the analytical resolution of coupled NLPDEs, offering a novel and distinct approach.…”

Section: Introductionmentioning

confidence: 99%

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Method of searching coupled optical solitons to magneto- optic waveguides having parabolic-nonlocal law of refractive index

Yomba

2024

Phys. Scr.

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Numerous methodologies employed for the exploration of soliton solutions within nonlinear models demonstrate considerable efficacy and efficiency in addressing individual non- linear partial differential equations (NLPDEs). However, their efficacy diminishes when applied to interconnected NLPDEs, owing to the presence of interaction terms in the coupled equations. Consequently, deriving exact solutions for such coupled equations presents a formidable challenge. In response to this challenge, several researchers have endeavored to solve coupled equations by assuming a proportional relationship between the solution in one line and that in another line, resulting in the imposition of excessive constraints and the subsequent reduction of coupled equations to a single equation. Regrettably, this approach compromises the fidelity of the physical phenomena that these equations aim to describe. In contrast, we propose a method characterized by its simplicity and directness, providing a more authentic and insightful analytical perspective for the investigation of coupled NLPDEs. The innovation lies in its capability to simultaneously propagate different types of solitons in two lines with a single operation, while also enabling the natural emergence of analogous solitons in both systems under minimal constraints. We apply this method to scrutinize the propagation of a diverse range of novel coupled progressive solitons in magneto-optical waveguides featuring a parabolic-nonlocal law of nonlinearity and governed by coupled nonlinear Schr ̈odinger equations. The resultant solitons, depicted through detailed 2D and 3D visualizations in Figures 1-12 demonstrate a multitude of coupled soliton forms, several of which are novel in the field.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Method of searching coupled optical solitons to magneto- optic waveguides having parabolic-nonlocal law of refractive index

Yomba

2024

Phys. Scr.

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“…Solitons play important roles in the existing structure of today's transmission technology, which are widely used in the optical fibers and telecommunications industries [1][2][3][4][5][6]. Under the combined action of group dispersion effect and nonlinear effect, solitons can propagate across intercontinental distances.…”

Section: Introductionmentioning

confidence: 99%

Optical solitons of Sasa-Satsuma model in birefringent fibers

Zhang¹

2022

Preprint

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This paper studies the propagation of optical solitons of the Sasa-Satsuma model in birefringent fibers. By the complete discrimination system for polynomial, we get three types of optical wave patterns for the model, where singular rational patterns and elliptic functions double periodic patterns are new propagation patterns. Besides, we show the temporal-space structures and propagation properties for some patterns with specific parameter values by drawing graphs.

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“…The magneto-waveguides with QC nonlinearity consist of polarization-preserving fibers as well as birefringent fibers. Now, we are observing a little shift of attention in the literature to the propagation of solitons in magnetooptic waveguides as the advancements in the telecommunication industries have rendered possible the mitigation of the soliton clutter, the control of the internet bottleneck and other detrimental features [14][15][16][17][18]. It is important to mention that magneto-optic waveguides have specific properties in comparison with waveguides made of other dielectric materials [19].…”

Section: Introductionmentioning

confidence: 99%

Coupled sn-cn, sn-dn, cn-dn Jacobi elliptic functions and solitons solutions in magneto-optic waveguides with quadratic-cubic nonlinearity

Yomba¹

2022

Phys. Scr.

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The current paper is dedicated to the study of the propagation of progressive solitons in magneto-optical waveguides that carry the quartic-cubic nonlinearity described by a coupled system of of nonlinear Schrödinger equations. In this direction, we take the help of a modiﬁed F-expansion method which allows us to widen the class of solutions to these coupled equations and permit the propagation of diﬀerent waves in the two channels. First of all, we constructed the solutions in terms of Jacobi elliptic functions in the forms of dn−sn, dn−cn, and cn − sn. After that, we obtained the progressive soliton solutions when these functions approached their limiting values with regards to the modulus of ellipticity. The progressive solutions include bright-dark soliton, bright-bright soliton, dark-dark soliton, bright-front soliton, dark-front soliton. In addition, we present the Figures 1-6 which graphically exhibit the representative structures of each explicit solution for some special parameter values.

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Solitons and conservation laws in magneto–optic waveguides having parabolic–nonlocal law of refractive index

Cited by 22 publications

References 11 publications

Method of searching coupled optical solitons to magneto- optic waveguides having parabolic-nonlocal law of refractive index

Method of searching coupled optical solitons to magneto- optic waveguides having parabolic-nonlocal law of refractive index

Optical solitons of Sasa-Satsuma model in birefringent fibers

Coupled sn-cn, sn-dn, cn-dn Jacobi elliptic functions and solitons solutions in magneto-optic waveguides with quadratic-cubic nonlinearity

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