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Keywords = Fokas–Lenells equations

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18 pages, 1227 KiB  
Article
Dispersive Optical Solitons for Stochastic Fokas-Lenells Equation With Multiplicative White Noise
by Elsayed M. E. Zayed, Mahmoud El-Horbaty, Mohamed E. M. Alngar and Mona El-Shater
Eng 2022, 3(4), 523-540; https://doi.org/10.3390/eng3040037 - 28 Nov 2022
Cited by 16 | Viewed by 2094
Abstract
For the first time, we study the Fokas–Lenells equation in polarization preserving fibers with multiplicative white noise in Itô sense. Four integration algorithms are applied, namely, the method of modified simple equation (MMSE), the method of sine-cosine (MSC), the method of Jacobi elliptic [...] Read more.
For the first time, we study the Fokas–Lenells equation in polarization preserving fibers with multiplicative white noise in Itô sense. Four integration algorithms are applied, namely, the method of modified simple equation (MMSE), the method of sine-cosine (MSC), the method of Jacobi elliptic equation (MJEE) and ansatze involving hyperbolic functions. Jacobi-elliptic function solutions, bright, dark, singular, combo dark-bright and combo bright-dark solitons are presented. Full article
(This article belongs to the Special Issue Feature Papers in Eng 2022)
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7 pages, 1220 KiB  
Article
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 - 4 Sep 2022
Cited by 6 | Viewed by 1691
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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11 pages, 263 KiB  
Article
Lie Symmetries and Conservation Laws of Fokas–Lenells Equation and Two Coupled Fokas–Lenells Equations by the Symmetry/Adjoint Symmetry Pair Method
by Lihua Zhang, Gangwei Wang, Qianqian Zhao and Lingshu Wang
Symmetry 2022, 14(2), 238; https://doi.org/10.3390/sym14020238 - 26 Jan 2022
Cited by 8 | Viewed by 2086
Abstract
The Fokas–Lenells equation and its multi-component coupled forms have attracted the attention of many mathematical physicists. The Fokas–Lenells equation and two coupled Fokas–Lenells equations are investigated from the perspective of Lie symmetries and conservation laws. The three systems have been turned into real [...] Read more.
The Fokas–Lenells equation and its multi-component coupled forms have attracted the attention of many mathematical physicists. The Fokas–Lenells equation and two coupled Fokas–Lenells equations are investigated from the perspective of Lie symmetries and conservation laws. The three systems have been turned into real multi-component coupled systems by appropriate transformations. By procedures of symmetry analysis, Lie symmetries of the three real systems are obtained. Explicit conservation laws are constructed using the symmetry/adjoint symmetry pair method, which depends on Lie symmetries and adjoint symmetries. The relationships between the multiplier and the adjoint symmetry are investigated. Full article
11 pages, 1365 KiB  
Article
Numerical Simulation of Cubic-Quartic Optical Solitons with Perturbed Fokas–Lenells Equation Using Improved Adomian Decomposition Algorithm
by Alyaa A. Al-Qarni, Huda O. Bakodah, Aisha A. Alshaery, Anjan Biswas, Yakup Yıldırım, Luminita Moraru and Simona Moldovanu
Mathematics 2022, 10(1), 138; https://doi.org/10.3390/math10010138 - 4 Jan 2022
Cited by 9 | Viewed by 2123
Abstract
The current manuscript displays elegant numerical results for cubic-quartic optical solitons associated with the perturbed Fokas–Lenells equations. To do so, we devise a generalized iterative method for the model using the improved Adomian decomposition method (ADM) and further seek validation from certain well-known [...] Read more.
The current manuscript displays elegant numerical results for cubic-quartic optical solitons associated with the perturbed Fokas–Lenells equations. To do so, we devise a generalized iterative method for the model using the improved Adomian decomposition method (ADM) and further seek validation from certain well-known results in the literature. As proven, the proposed scheme is efficient and possess a high level of accuracy. Full article
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19 pages, 5437 KiB  
Article
New Exact Solutions of the New Hamiltonian Amplitude-Equation and Fokas Lenells Equation
by Seyma Tuluce Demiray and Hasan Bulut
Entropy 2015, 17(9), 6025-6043; https://doi.org/10.3390/e17096025 - 27 Aug 2015
Cited by 44 | Viewed by 5252
Abstract
In this paper, exact solutions of the new Hamiltonian amplitude equation and Fokas-Lenells equation are successfully obtained. The extended trial equation method (ETEM) and generalized Kudryashov method (GKM) are applied to find several exact solutions of the new Hamiltonian amplitude equation and Fokas-Lenells [...] Read more.
In this paper, exact solutions of the new Hamiltonian amplitude equation and Fokas-Lenells equation are successfully obtained. The extended trial equation method (ETEM) and generalized Kudryashov method (GKM) are applied to find several exact solutions of the new Hamiltonian amplitude equation and Fokas-Lenells equation. Primarily, we seek some exact solutions of the new Hamiltonian amplitude equation and Fokas-Lenells equation by using ETEM. Then, we research dark soliton solutions of the new Hamiltonian amplitude equation and Fokas-Lenells equation by using GKM. Lastly, according to the values of some parameters, we draw two and three dimensional graphics of imaginary and real values of certain solutions found by utilizing both methods. Full article
(This article belongs to the Section Complexity)
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