Research

11 pages, 270 KiB

Open AccessCommunication

Optical Soliton Perturbation with Parabolic Law Nonlinearity

by Ahmed H. Arnous, Islam Samir, Anjan Biswas, Oswaldo González-Gaxiola, Luminita Moraru, Catalina Iticescu, Simona Moldovanu and Abdulah A. Alghamdi

Universe 2023, 9(3), 155; https://doi.org/10.3390/universe9030155 - 21 Mar 2023

Cited by 3 | Viewed by 833

Abstract

This paper recovers a broad spectrum of optical solitons for the perturbed nonlinear Schrödinger’s equation having a dual-power law of nonlinearity. The perturbation terms are from inter-modal dispersion and self-frequency shift. The integration scheme is the improved extended tanh function approach. The parameter [...] Read more.

This paper recovers a broad spectrum of optical solitons for the perturbed nonlinear Schrödinger’s equation having a dual-power law of nonlinearity. The perturbation terms are from inter-modal dispersion and self-frequency shift. The integration scheme is the improved extended tanh function approach. The parameter constraints that naturally emerge are also enumerated. Full article

(This article belongs to the Special Issue Research on Optical Soliton Perturbation)

13 pages, 277 KiB

Open AccessArticle

Highly Dispersive Optical Solitons with Four Forms of Self-Phase Modulation

by Ahmed M. Elsherbeny, Ahmed H. Arnous, Anjan Biswas, Oswaldo González-Gaxiola, Luminita Moraru, Simona Moldovanu, Catalina Iticescu and Hashim M. Alshehri

Universe 2023, 9(1), 51; https://doi.org/10.3390/universe9010051 - 12 Jan 2023

Cited by 9 | Viewed by 991

Abstract

This paper implements the enhanced Kudryashov approach to retrieve highly dispersive optical solitons and study it with four nonlinear forms. These are the power law, generalized quadratic-cubic law, triple-power law, and the generalized non-local law. This approach reveals bright and singular optical solitons [...] Read more.

This paper implements the enhanced Kudryashov approach to retrieve highly dispersive optical solitons and study it with four nonlinear forms. These are the power law, generalized quadratic-cubic law, triple-power law, and the generalized non-local law. This approach reveals bright and singular optical solitons along with the respective parameter constraints. Full article

(This article belongs to the Special Issue Research on Optical Soliton Perturbation)

9 pages, 1308 KiB

Open AccessCommunication

Dispersive Optical Solitons with Schrödinger–Hirota Equation by Laplace-Adomian Decomposition Approach

by O. González-Gaxiola, Anjan Biswas, Luminita Moraru and Simona Moldovanu

Universe 2023, 9(1), 19; https://doi.org/10.3390/universe9010019 - 29 Dec 2022

Cited by 5 | Viewed by 1317

Abstract

This paper studies dispersive bright and dark optical solitons, modeled by the Schrödinger–Hirota equation, numerically by the aid of the Adomian decomposition. The surface plots of the algorithm yielded an impressively small measure. The effects of soliton radiation are ignored. Full article

(This article belongs to the Special Issue Research on Optical Soliton Perturbation)

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10 pages, 811 KiB

Open AccessCommunication

Optical Solitons and Conservation Laws for the Concatenation Model: Undetermined Coefficients and Multipliers Approach

by Anjan Biswas, Jose Vega-Guzman, Abdul H. Kara, Salam Khan, Houria Triki, O. González-Gaxiola, Luminita Moraru and Puiu Lucian Georgescu

Universe 2023, 9(1), 15; https://doi.org/10.3390/universe9010015 - 27 Dec 2022

Cited by 35 | Viewed by 1453

Abstract

This paper retrieves an optical 1–soliton solution to a model that is written as a concatenation of the Lakshmanan–Porsezian–Daniel model and Sasa–Satsuma equation. The method of undetermined coefficients obtains a full spectrum of 1–soliton solutions. The multiplier approach yields the conserved densities, which [...] Read more.

This paper retrieves an optical 1–soliton solution to a model that is written as a concatenation of the Lakshmanan–Porsezian–Daniel model and Sasa–Satsuma equation. The method of undetermined coefficients obtains a full spectrum of 1–soliton solutions. The multiplier approach yields the conserved densities, which subsequently lead to the conserved quantities from the bright 1–soliton solution. Full article

(This article belongs to the Special Issue Research on Optical Soliton Perturbation)

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13 pages, 311 KiB

Open AccessArticle

Ricci Soliton and Certain Related Metrics on a Three-Dimensional Trans-Sasakian Manifold

by Zhizhi Chen, Yanlin Li, Sumanjit Sarkar, Santu Dey and Arindam Bhattacharyya

Universe 2022, 8(11), 595; https://doi.org/10.3390/universe8110595 - 11 Nov 2022

Cited by 8 | Viewed by 1132

Abstract

In this article, a Ricci soliton and *-conformal Ricci soliton are examined in the framework of trans-Sasakian three-manifold. In the beginning of the paper, it is shown that a three-dimensional trans-Sasakian manifold of type

(α, β)

admits a Ricci soliton [...] Read more.

In this article, a Ricci soliton and *-conformal Ricci soliton are examined in the framework of trans-Sasakian three-manifold. In the beginning of the paper, it is shown that a three-dimensional trans-Sasakian manifold of type

(α, β)

admits a Ricci soliton where the covariant derivative of potential vector field V in the direction of unit vector field

ξ

is orthogonal to

ξ

. It is also demonstrated that if the structure functions meet

α^{2} = β^{2}

, then the covariant derivative of V in the direction of

ξ

is a constant multiple of

ξ

. Furthermore, the nature of scalar curvature is evolved when the manifold of type

(α, β)

satisfies *-conformal Ricci soliton, provided

α \neq 0

. Finally, an example is presented to verify the findings. Full article

(This article belongs to the Special Issue Research on Optical Soliton Perturbation)

19 pages, 650 KiB

Open AccessArticle

Construction of Exact Solutions for Gilson–Pickering Model Using Two Different Approaches

by Hamood Ur Rehman, Aziz Ullah Awan, ElSayed M. Tag-ElDin, Uzma Bashir and Seham Ayesh Allahyani

Universe 2022, 8(11), 592; https://doi.org/10.3390/universe8110592 - 08 Nov 2022

Cited by 7 | Viewed by 1280

Abstract

In this paper, the extended simple equation method (ESEM) and the generalized Riccati equation mapping (GREM) method are applied to the nonlinear third-order Gilson–Pickering (GP) model to obtain a variety of new exact wave solutions. With the suitable selection of parameters involved in [...] Read more.

In this paper, the extended simple equation method (ESEM) and the generalized Riccati equation mapping (GREM) method are applied to the nonlinear third-order Gilson–Pickering (GP) model to obtain a variety of new exact wave solutions. With the suitable selection of parameters involved in the model, some familiar physical governing models such as the Camassa–Holm (CH) equation, the Fornberg–Whitham (FW) equation, and the Rosenau–Hyman (RH) equation are obtained. The graphical representation of solutions under different constraints shows the dark, bright, combined dark–bright, periodic, singular, and kink soliton. For the graphical representation, 3D plots, contour plots, and 2D plots of some acquired solutions are illustrated. The obtained wave solutions motivate researchers to enhance their theories to the best of their capacities and to utilize the outcomes in other nonlinear cases. The executed methods are shown to be practical and straightforward for approaching the considered equation and may be utilized to study abundant types of NLEEs arising in physics, engineering, and applied sciences. Full article

(This article belongs to the Special Issue Research on Optical Soliton Perturbation)

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12 pages, 2299 KiB

Open AccessArticle

Two Analytical Schemes for the Optical Soliton Solution of the (2 + 1) Hirota–Maccari System Observed in Single-Mode Fibers

by Neslihan Ozdemir, Aydin Secer, Muslum Ozisik and Mustafa Bayram

Universe 2022, 8(11), 584; https://doi.org/10.3390/universe8110584 - 04 Nov 2022

Cited by 5 | Viewed by 1176

Abstract

In this scientific research article, the new Kudryashov method and the tanh-coth method, which have not been applied before, are employed to construct analytical and soliton solutions of the

(2 + 1)

-dimensional Hirota–Maccari system. The

(2 + 1)

[...] Read more.

In this scientific research article, the new Kudryashov method and the tanh-coth method, which have not been applied before, are employed to construct analytical and soliton solutions of the

(2 + 1)

-dimensional Hirota–Maccari system. The

(2 + 1)

-dimensional Hirota–Maccari system is a special kind of nonlinear Schrödinger equation (NLSEs) that models the motion of isolated waves localized in a small part of space, and is used in such various fields as fiber optics telecommunication systems, nonlinear optics, plasma physics, and hydrodynamics. In addition, the Hirota–Maccari system defines the dynamical characters of femtosecond soliton pulse propagation in single-mode fibers. Analytical solutions of the model are successfully acquired with the assistance of symbolic computation utilizing these methods. Finally, 3D, 2D, and contour graphs of solutions are depicted at specific values of parameters. It is shown that the new Kudryashov method and the tanh-coth method are uncomplicated, very effective, easily applicable, reliable, and indeed vital mathematical tools in solving nonlinear models. Full article

(This article belongs to the Special Issue Research on Optical Soliton Perturbation)

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18 pages, 6319 KiB

Open AccessArticle

Improved Soliton Solutions of Generalized Fifth Order Time-Fractional KdV Models: Laplace Transform with Homotopy Perturbation Algorithm

by Mubashir Qayyum, Efaza Ahmad, Muhammad Bilal Riaz and Jan Awrejcewicz

Universe 2022, 8(11), 563; https://doi.org/10.3390/universe8110563 - 27 Oct 2022

Cited by 7 | Viewed by 1273

Abstract

The main purpose of this research is to propose a new methodology to observe a class of time-fractional generalized fifth-order Korteweg–de Vries equations. Laplace transform along with a homotopy perturbation algorithm is utilized for the solution and analysis purpose in the current study. [...] Read more.

The main purpose of this research is to propose a new methodology to observe a class of time-fractional generalized fifth-order Korteweg–de Vries equations. Laplace transform along with a homotopy perturbation algorithm is utilized for the solution and analysis purpose in the current study. This extended technique provides improved and convergent series solutions through symbolic computation. The proposed methodology is applied to time-fractional Sawada–Kotera, Ito, Lax’s, and Kaup–Kupershmidt models, which are induced from a generalized fifth-order KdV equation. For validity purposes, obtained and existing results at integral orders are compared. Convergence analysis was also performed by computing solutions and errors at different values in a fractional domain. Dynamic behavior of the fractional parameter is also studied graphically. Simulations affirm the dominance of the proposed algorithm in terms of accuracy and fewer computations as compared to other available schemes for fractional KdVs. Hence, the projected algorithm can be utilized for more advanced fractional models in physics and engineering. Full article

(This article belongs to the Special Issue Research on Optical Soliton Perturbation)

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8 pages, 937 KiB

Open AccessArticle

Quiescent Optical Solitons with Kudryashov’s Generalized Quintuple-Power and Nonlocal Nonlinearity Having Nonlinear Chromatic Dispersion

by Ahmed H. Arnous, Taher A. Nofal, Anjan Biswas, Salam Khan and Luminita Moraru

Universe 2022, 8(10), 501; https://doi.org/10.3390/universe8100501 - 22 Sep 2022

Cited by 9 | Viewed by 1004

Abstract

The paper derives stationary optical solitons with nonlinear chromatic dispersion. A nonlocal form of nonlinearity and quintuple power–law of nonlinearity are considered. The Kudryashov’s integration scheme enables to retrieve such solitons. A plethora of solitons come with this algorithm. Full article

(This article belongs to the Special Issue Research on Optical Soliton Perturbation)

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7 pages, 1220 KiB

Open AccessArticle

Cubic–Quartic Optical Soliton Perturbation for Fokas–Lenells Equation with Power Law by Semi-Inverse Variation

by Anjan Biswas, Jawonki Moseley, Salam Khan, Luminita Moraru, Simona Moldovanu, Catalina Iticescu and Hashim M. Alshehri

Universe 2022, 8(9), 460; https://doi.org/10.3390/universe8090460 - 04 Sep 2022

Cited by 4 | Viewed by 1149

Abstract

The current work addresses cubic–quartic solitons to compensate for the low count of the chromatic dispersion that is one of the major hindrances of soliton transmission through optical fibers. Thus, the present paper handles the cubic–quartic version of the perturbed Fokas–Lenells equation that [...] Read more.

The current work addresses cubic–quartic solitons to compensate for the low count of the chromatic dispersion that is one of the major hindrances of soliton transmission through optical fibers. Thus, the present paper handles the cubic–quartic version of the perturbed Fokas–Lenells equation that governs soliton communications across trans-oceanic and trans-continental distances. The model is also considered with the power-law form of nonlinear refractive index that is a sequel to the previously reported result. This is a tremendous advancement to the previously known result that was only with the Kerr-law form of nonlinear refractive index. The present paper mainly contributes by generalizing the Kerr law of nonlinearity to the power law of nonlinearity. The prior results therefore fall back as a special case to the results of this paper. The semi-inverse variational principle yields a bright 1-soliton solution that is imperative for the telecommunication engineers to carry out experimental investigation before the rubber meets the road. Hamiltonian perturbation terms are included that come with maximum intensity. The soliton amplitude–width relation is retrievable from a polynomial equation with arbitrary degree. The parameter constraints are also identified for the soliton to exist. Full article

(This article belongs to the Special Issue Research on Optical Soliton Perturbation)

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19 pages, 6848 KiB

Open AccessArticle

New Soliton Solutions of Time-Fractional Korteweg–de Vries Systems

by Mubashir Qayyum, Efaza Ahmad, Muhammad Bilal Riaz, Jan Awrejcewicz and Syed Tauseef Saeed

Universe 2022, 8(9), 444; https://doi.org/10.3390/universe8090444 - 26 Aug 2022

Cited by 8 | Viewed by 1400

Abstract

Model construction for different physical situations, and developing their solutions, are the major characteristics of the scientific work in physics and engineering. Korteweg–de Vries (KdV) models are very important due to their ability to capture different physical situations such as thin film flows [...] Read more.

Model construction for different physical situations, and developing their solutions, are the major characteristics of the scientific work in physics and engineering. Korteweg–de Vries (KdV) models are very important due to their ability to capture different physical situations such as thin film flows and waves on shallow water surfaces. In this work, a new approach for predicting and analyzing nonlinear time-fractional coupled KdV systems is proposed based on Laplace transform and homotopy perturbation along with Caputo fractional derivatives. This algorithm provides a convergent series solution by applying simple steps through symbolic computations. The efficiency of the proposed algorithm is tested against different nonlinear time-fractional KdV systems, including dispersive long wave and generalized Hirota–Satsuma KdV systems. For validity purposes, the obtained results are compared with the existing solutions from the literature. The convergence of the proposed algorithm over the entire fractional domain is confirmed by finding solutions and errors at various values of fractional parameters. Numerical simulations clearly reassert the supremacy and capability of the proposed technique in terms of accuracy and fewer computations as compared to other available schemes. Analysis reveals that the projected scheme is reliable and hence can be utilized with other kernels in more advanced systems in physics and engineering. Full article

(This article belongs to the Special Issue Research on Optical Soliton Perturbation)

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