Dynamics of M-truncated optical solitons and other solutions to the fractional Kudryashov’s equation
The study of soliton theory plays a crucial role in the telecommunication industry’s utilization of nonlinear optics. The principal area of research in the field of optical solitons revolves around optical fibers, metamaterials, metasurfaces, magneto-optic waveguides, and other related technologies....
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| Format: | Article |
| Language: | English |
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Elsevier
2024-03-01
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| Series: | Results in Physics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2211379724001852 |
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| author | Usman Younas Fengping Yao Naila Nasreen Aziz Khan Thabet Abdeljawad |
| author_facet | Usman Younas Fengping Yao Naila Nasreen Aziz Khan Thabet Abdeljawad |
| author_sort | Usman Younas |
| collection | DOAJ |
| description | The study of soliton theory plays a crucial role in the telecommunication industry’s utilization of nonlinear optics. The principal area of research in the field of optical solitons revolves around optical fibers, metamaterials, metasurfaces, magneto-optic waveguides, and other related technologies. Therefore, the examination of these solitons received significant attention from scholars in recent years. Optical solitons refer to electromagnetic waves that are confined within nonlinear dispersive medium, wherein the balance between dispersion and nonlinearity effects enables the intensity to remain constant. In this manuscript, the dynamical behavior of Kudryashov’s equation is discussed with the assistance of truncated M-fractional derivative. Kudryashov’s equation is a mathematical model utilized to characterize complex phenomena in telecommunications and transmission technology. It describes the propagation of nonlinear pulses in optical fibers. Different forms of soliton solutions like bright, dark, singular and combo solitions have been extracted. Moreover, hyperbolic, periodic and Jacobi elliptic function solutions are recovered. Two recently modern integration tools like Φ6-expansion method and modified generalized exponential rational function method have been adopted to recover the solutions. The used methods not only provides previously extracted solutions but also secures new solutions. In order to visually depict the output, a variety of graphs featuring distinct shapes are produced in response to appropriate parameter values. The results obtained from this research indicate that the chosen methodologies are effective in improving the understanding of nonlinear dynamical phenomena. A large number of engineers who employ engineering models are expected to find this research interesting. The results demonstrate that the selected methods are practical, straightforward to implement, and applicable to intricate systems across numerous domains, with a specific emphasis on the field of optical fibers. The findings indicate that the system may contain a considerable number of soliton structures. |
| first_indexed | 2024-03-07T22:00:48Z |
| format | Article |
| id | doaj.art-1905c188caae4ceb9e4d1dc4e29394eb |
| institution | Directory Open Access Journal |
| issn | 2211-3797 |
| language | English |
| last_indexed | 2024-04-24T23:18:01Z |
| publishDate | 2024-03-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Physics |
| spelling | doaj.art-1905c188caae4ceb9e4d1dc4e29394eb2024-03-17T07:53:43ZengElsevierResults in Physics2211-37972024-03-0158107503Dynamics of M-truncated optical solitons and other solutions to the fractional Kudryashov’s equationUsman Younas0Fengping Yao1Naila Nasreen2Aziz Khan3Thabet Abdeljawad4Department of Mathematics, Shanghai University, No. 99 Shangda Road, Shanghai 200444, China; Newtouch Center for Mathematics of Shanghai University, Shanghai 200444, ChinaDepartment of Mathematics, Shanghai University, No. 99 Shangda Road, Shanghai 200444, China; Newtouch Center for Mathematics of Shanghai University, Shanghai 200444, ChinaFaculty of Science, Jiangsu University, Zhenjiang 212013, Jiangsu, ChinaDepartment of Mathematics and Sciences, Prince Sultan University, Riyadh, Saudi ArabiaDepartment of Mathematics and Sciences, Prince Sultan University, Riyadh, Saudi Arabia; Department of Medical Research, China Medical University, Taichung 40402, Taiwan; Department of Mathematics, Kyung Hee University, Seoul, 02447, Republic of Korea; Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, South Africa; Corresponding author.The study of soliton theory plays a crucial role in the telecommunication industry’s utilization of nonlinear optics. The principal area of research in the field of optical solitons revolves around optical fibers, metamaterials, metasurfaces, magneto-optic waveguides, and other related technologies. Therefore, the examination of these solitons received significant attention from scholars in recent years. Optical solitons refer to electromagnetic waves that are confined within nonlinear dispersive medium, wherein the balance between dispersion and nonlinearity effects enables the intensity to remain constant. In this manuscript, the dynamical behavior of Kudryashov’s equation is discussed with the assistance of truncated M-fractional derivative. Kudryashov’s equation is a mathematical model utilized to characterize complex phenomena in telecommunications and transmission technology. It describes the propagation of nonlinear pulses in optical fibers. Different forms of soliton solutions like bright, dark, singular and combo solitions have been extracted. Moreover, hyperbolic, periodic and Jacobi elliptic function solutions are recovered. Two recently modern integration tools like Φ6-expansion method and modified generalized exponential rational function method have been adopted to recover the solutions. The used methods not only provides previously extracted solutions but also secures new solutions. In order to visually depict the output, a variety of graphs featuring distinct shapes are produced in response to appropriate parameter values. The results obtained from this research indicate that the chosen methodologies are effective in improving the understanding of nonlinear dynamical phenomena. A large number of engineers who employ engineering models are expected to find this research interesting. The results demonstrate that the selected methods are practical, straightforward to implement, and applicable to intricate systems across numerous domains, with a specific emphasis on the field of optical fibers. The findings indicate that the system may contain a considerable number of soliton structures.http://www.sciencedirect.com/science/article/pii/S2211379724001852Fractional Kudryashov’s equationOptical solitonsΦ6-expansion methodModified generalized exponential rational function methodJacobi elliptic function solutions |
| spellingShingle | Usman Younas Fengping Yao Naila Nasreen Aziz Khan Thabet Abdeljawad Dynamics of M-truncated optical solitons and other solutions to the fractional Kudryashov’s equation Results in Physics Fractional Kudryashov’s equation Optical solitons Φ6-expansion method Modified generalized exponential rational function method Jacobi elliptic function solutions |
| title | Dynamics of M-truncated optical solitons and other solutions to the fractional Kudryashov’s equation |
| title_full | Dynamics of M-truncated optical solitons and other solutions to the fractional Kudryashov’s equation |
| title_fullStr | Dynamics of M-truncated optical solitons and other solutions to the fractional Kudryashov’s equation |
| title_full_unstemmed | Dynamics of M-truncated optical solitons and other solutions to the fractional Kudryashov’s equation |
| title_short | Dynamics of M-truncated optical solitons and other solutions to the fractional Kudryashov’s equation |
| title_sort | dynamics of m truncated optical solitons and other solutions to the fractional kudryashov s equation |
| topic | Fractional Kudryashov’s equation Optical solitons Φ6-expansion method Modified generalized exponential rational function method Jacobi elliptic function solutions |
| url | http://www.sciencedirect.com/science/article/pii/S2211379724001852 |
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