Cubic-quartic optical solitons with polarization-mode dispersion by the improved adomian decomposition scheme
This research investigates the numerical computation of cubic-quartic optical solitons in birefringent fibers in accordance with Kerr's law. Utilizing the Improved Adomian Decomposition Method (IADM), the study improves the solution of complex-valued nonlinear evolution equations. It identifies...
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| Language: | English |
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Elsevier
2025-06-01
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| Series: | MethodsX |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2215016125000391 |
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| author | Afrah M. Almalki A.A. AlQarni H.O. Bakodah A.A. Alshaery Ahmed H. Arnous Anjan Biswas |
| author_facet | Afrah M. Almalki A.A. AlQarni H.O. Bakodah A.A. Alshaery Ahmed H. Arnous Anjan Biswas |
| author_sort | Afrah M. Almalki |
| collection | DOAJ |
| description | This research investigates the numerical computation of cubic-quartic optical solitons in birefringent fibers in accordance with Kerr's law. Utilizing the Improved Adomian Decomposition Method (IADM), the study improves the solution of complex-valued nonlinear evolution equations. It identifies a strong correlation between numerical results and earlier analytical soliton expressions from Zahran and Bekir. The analysis highlights impressively low computational errors, confirming IADM's effectiveness in delivering accurate solutions. This method decomposes both linear and nonlinear differential equations into simpler sub-problems, enabling the extraction of approximate analytical solutions without the need for linearization or perturbation techniques. IADM's adaptability suggests its potential for application in various domains, particularly in the optimization and design of optical communication systems. • The research utilizes both the Adomian Decomposition Method (ADM) and its enhanced version (IADM) to solve the Gerdjikov-Ivanov equation. • Numerical simulations validate the accuracy and stability of these methods, with IADM showing superior convergence. • The study underscores the importance of these methods in improving optical communication systems and other nonlinear applications. |
| format | Article |
| id | doaj-art-d56d0db3d8e343bdbd983d7e73291aaa |
| institution | Kabale University |
| issn | 2215-0161 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | Elsevier |
| record_format | Article |
| series | MethodsX |
| spelling | doaj-art-d56d0db3d8e343bdbd983d7e73291aaa2025-02-06T05:11:49ZengElsevierMethodsX2215-01612025-06-0114103191Cubic-quartic optical solitons with polarization-mode dispersion by the improved adomian decomposition schemeAfrah M. Almalki0A.A. AlQarni1H.O. Bakodah2A.A. Alshaery3Ahmed H. Arnous4Anjan Biswas5Department of Mathematics and Statistics, College of Science, University of Jeddah, Jeddah, Saudi ArabiaDepartment of Mathematics, College of Science, University of Bisha, P.O. Box 551, Bisha 61922, Saudi ArabiaDepartment of Mathematics and Statistics, College of Science, University of Jeddah, Jeddah, Saudi ArabiaDepartment of Mathematics and Statistics, College of Science, University of Jeddah, Jeddah, Saudi ArabiaDepartment of Engineering Mathematics and Physics, Higher Institute of Engineering, El Shorouk Academy, Cairo, EgyptDepartment of Mathematics and Physics, Grambling State University, Grambling, LA 71245-2715, USA; Department of Applied Sciences, Cross-Border Faculty of Humanities, Economics and Engineering, Dunarea de Jos University of Galati, 111 Domneasca Street, Galati 800201, Romania; Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Medunsa 0204, Pretoria, South Africa; Corresponding author at: Department of Mathematics and Physics, Grambling State University, Grambling, LA 71245-2715, USA.This research investigates the numerical computation of cubic-quartic optical solitons in birefringent fibers in accordance with Kerr's law. Utilizing the Improved Adomian Decomposition Method (IADM), the study improves the solution of complex-valued nonlinear evolution equations. It identifies a strong correlation between numerical results and earlier analytical soliton expressions from Zahran and Bekir. The analysis highlights impressively low computational errors, confirming IADM's effectiveness in delivering accurate solutions. This method decomposes both linear and nonlinear differential equations into simpler sub-problems, enabling the extraction of approximate analytical solutions without the need for linearization or perturbation techniques. IADM's adaptability suggests its potential for application in various domains, particularly in the optimization and design of optical communication systems. • The research utilizes both the Adomian Decomposition Method (ADM) and its enhanced version (IADM) to solve the Gerdjikov-Ivanov equation. • Numerical simulations validate the accuracy and stability of these methods, with IADM showing superior convergence. • The study underscores the importance of these methods in improving optical communication systems and other nonlinear applications.http://www.sciencedirect.com/science/article/pii/S2215016125000391The improved Adomian decomposition method |
| spellingShingle | Afrah M. Almalki A.A. AlQarni H.O. Bakodah A.A. Alshaery Ahmed H. Arnous Anjan Biswas Cubic-quartic optical solitons with polarization-mode dispersion by the improved adomian decomposition scheme MethodsX The improved Adomian decomposition method |
| title | Cubic-quartic optical solitons with polarization-mode dispersion by the improved adomian decomposition scheme |
| title_full | Cubic-quartic optical solitons with polarization-mode dispersion by the improved adomian decomposition scheme |
| title_fullStr | Cubic-quartic optical solitons with polarization-mode dispersion by the improved adomian decomposition scheme |
| title_full_unstemmed | Cubic-quartic optical solitons with polarization-mode dispersion by the improved adomian decomposition scheme |
| title_short | Cubic-quartic optical solitons with polarization-mode dispersion by the improved adomian decomposition scheme |
| title_sort | cubic quartic optical solitons with polarization mode dispersion by the improved adomian decomposition scheme |
| topic | The improved Adomian decomposition method |
| url | http://www.sciencedirect.com/science/article/pii/S2215016125000391 |
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