Optical solitons of the model with arbitrary refractive index

Kudryashov, Nikolay A.

doi:10.1016/j.ijleo.2020.165767

Cited by 13 publications

(5 citation statements)

References 32 publications

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“…In figure 3, we demonstrated several plots of |Q 2 (x, t)| 2 in equation (26). According to figure 4(c), the soliton travels to the left through the positive x-axis direction as t increases.…”

Section: Resultsmentioning

confidence: 93%

“…Recently, some models have been derived by reckoning without the term chromatic dispersion and adding higher-order nonlinear terms from the literature. Some of the models developed in this context are: NLSE having arbitrary refractive index [25][26][27][28], NLSE including anti-cubic nonlinearity [29], NLSE having Kudryashovʼs sextic power-law of nonlinear refractive index [9,[30][31][32][33][34], cubic-quintic NLSE [35][36][37], NLSE with cubic-quintic-septic nonlinearities [38,39], NLSE with cubic-quintic-septic-nonic (CQSN) nonlinearities [5,[40][41][42].…”

Section: Introductionmentioning

confidence: 99%

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Optical soliton solutions of the nonlinear Schrödinger equation in the presence of chromatic dispersion with cubic-quintic-septic-nonicnonlinearities

Ozdemir,

Secer,

Ozisik

et al. 2023

Phys. Scr.

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In this study, one of our main subjects is the examination of optical solitons of the nonlinear Schrödinger equation having cubic-quintic-septic-nonic nonlinearities via the modified F-expansion method. The other subject is also the analysis of the impacts of some parameters in the model on the soliton shape, which is examined for the first time in this study. According to the modified F-expansion method, we select the suitable transformation to gain the nonlinear ordinary differential equation for the nonlinear Schrödinger equation having cubic-quintic-septic-nonic nonlinearities in the first stage. Then, we get a system consisting of linear equations in polynomial form with the aid of the modified F-expansion method. Various solution sets consisting of the parameters of the nonlinear Schrödinger equation having cubic-quintic-septic-nonic nonlinearities are achieved. Inserting the selected sets and transformations into the serial form of the presented method and utilizing the solutions of the auxiliary equation in the presented method, the optical soliton solutions of the model are derived. Furthermore, varied optical soliton solutions, such as anti-kink, singular, and bright, are achieved, and 3D and 2D projections of the generated soliton solutions have been illustrated. The impact of some parameters on each soliton behavior has also been examined. It is found that these parameters have a significant impact on the soliton structure.

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Section: Resultsmentioning

confidence: 93%

Section: Introductionmentioning

confidence: 99%

Optical soliton solutions of the nonlinear Schrödinger equation in the presence of chromatic dispersion with cubic-quintic-septic-nonicnonlinearities

Ozdemir,

Secer,

Ozisik

et al. 2023

Phys. Scr.

View full text Add to dashboard Cite

show abstract

“…-Set 5 The existence of this solution requires the following constraints among the coefficients of the (1) and (2) (26). We get the following progressive solitonic-type solutions…”

Section: Methods For Finding Combination Of Different Kinds Of Solito...mentioning

confidence: 99%

“…K 1 is an arbitrary parameter. We illustrate this family of solutions in the figures 11 using constraints on the parameters given in (26). We were able to retrieve the following coupled progressive solitons: bright-anti kink-solutions.…”

Section: Methods For Finding Combination Of Different Kinds Of Solito...mentioning

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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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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“…Recently, N. A. Kudryashov has suggested a number of forms for the self-phase modulation effect, which have sparked a great interest among physicists and telecommunication engineers [6][7][8][9][10][11][12][13][14][15][16]. The present work addresses soliton solutions of the governing nonlinear Schrödinger's equation, which come from one of the latest forms of refractive-index nonlinearity introduced by N. A.…”

Section: Introductionmentioning

confidence: 98%

Optical solitons and conservation laws associated with Kudryashov�s sextic power-law nonlinearity of refractive index

Zayed¹,

Shohib²,

Alngar³

et al. 2021

Ukr. J. Phys. Opt.

160

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We recover the cases of solutions in the shape of bright, dark and singular optical solitons for the self-phase modulation effect, which belongs to the type of N. A. Kudryashov's sextic power-law nonlinearity of refractive index. Three different integration schemes have been implemented. These are a unified Riccati equation, our new mapping scheme and our addendum to the common N. A. Kudryashov's method. All of the solitons are enlisted and the criterions of their existence are mentioned. Finally, we extract three appropriate conservation laws.

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Optical solitons of the model with arbitrary refractive index

Cited by 13 publications

References 32 publications

Optical soliton solutions of the nonlinear Schrödinger equation in the presence of chromatic dispersion with cubic-quintic-septic-nonicnonlinearities

Optical soliton solutions of the nonlinear Schrödinger equation in the presence of chromatic dispersion with cubic-quintic-septic-nonicnonlinearities

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

Optical solitons and conservation laws associated with Kudryashov�s sextic power-law nonlinearity of refractive index

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