Influence of the $ \beta $-fractional derivative on optical soliton solutions of the pure-quartic nonlinear Schrödinger equation with weak nonlocality
This study investigated the dynamics of a pure-quartic nonlinear Schrödinger equation incorporating a $ \beta $-fractional derivative and weak nonlocal effects prevalent in optical fiber systems. Using the improved modified extended tanh-function method, we obtained a diverse array of soliton soluti...
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| Language: | English |
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AIMS Press
2025-03-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2025344 |
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| author | Mahmoud Soliman Hamdy M. Ahmed Niveen Badra M. Elsaid Ramadan Islam Samir Soliman Alkhatib |
| author_facet | Mahmoud Soliman Hamdy M. Ahmed Niveen Badra M. Elsaid Ramadan Islam Samir Soliman Alkhatib |
| author_sort | Mahmoud Soliman |
| collection | DOAJ |
| description | This study investigated the dynamics of a pure-quartic nonlinear Schrödinger equation incorporating a $ \beta $-fractional derivative and weak nonlocal effects prevalent in optical fiber systems. Using the improved modified extended tanh-function method, we obtained a diverse array of soliton solutions, including bright, dark, and singular solitons, as well as hyperbolic, trigonometric, and Jacobi elliptic solutions. The main goal was to clarify how fractional derivatives, defined by the parameter $ \beta $, affect the characteristics and behavior of these soliton solutions. The key outcomes indicate that variations in the parameter $ \beta $ lead to substantial changes in soliton amplitude, shape, and propagation patterns. Graphical illustrations clearly depict these transformations, highlighting how fractional derivatives have a major impact on the properties of solitons. Crucially, for certain fractional orders, the localization and stability of solitons are enhanced, which is essential for accurate modeling of nonlocal and dispersive effects in optical fibers. This work not only enhances fundamental understanding of nonlinear wave phenomena within optical communication systems but also offers valuable insights into using fractional calculus for designing and optimizing advanced photonic devices. |
| format | Article |
| id | doaj-art-2d19ca202b5242d39d4d79a29529a387 |
| institution | DOAJ |
| issn | 2473-6988 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-2d19ca202b5242d39d4d79a29529a3872025-08-20T03:16:58ZengAIMS PressAIMS Mathematics2473-69882025-03-011037489750810.3934/math.2025344Influence of the $ \beta $-fractional derivative on optical soliton solutions of the pure-quartic nonlinear Schrödinger equation with weak nonlocalityMahmoud Soliman0Hamdy M. Ahmed1Niveen Badra2M. Elsaid Ramadan3Islam Samir4Soliman Alkhatib5Department of Physics and Mathematics Engineering, Faculty of Engineering, Ain Shams University, Cairo, EgyptDepartment of Physics and Engineering Mathematics, Higher Institute of Engineering, El Shorouk Academy, Cairo, EgyptDepartment of Physics and Mathematics Engineering, Faculty of Engineering, Ain Shams University, Cairo, EgyptDepartment of Mathematics, Faculty of Science, Islamic University of Madinah, Medina, Saudi ArabiaDepartment of Physics and Mathematics Engineering, Faculty of Engineering, Ain Shams University, Cairo, EgyptCollege of Engineering and Technology, American University in the Emirates (AUE), Dubai intel Academic City, P. O. Box 503000, Dubai, UAEThis study investigated the dynamics of a pure-quartic nonlinear Schrödinger equation incorporating a $ \beta $-fractional derivative and weak nonlocal effects prevalent in optical fiber systems. Using the improved modified extended tanh-function method, we obtained a diverse array of soliton solutions, including bright, dark, and singular solitons, as well as hyperbolic, trigonometric, and Jacobi elliptic solutions. The main goal was to clarify how fractional derivatives, defined by the parameter $ \beta $, affect the characteristics and behavior of these soliton solutions. The key outcomes indicate that variations in the parameter $ \beta $ lead to substantial changes in soliton amplitude, shape, and propagation patterns. Graphical illustrations clearly depict these transformations, highlighting how fractional derivatives have a major impact on the properties of solitons. Crucially, for certain fractional orders, the localization and stability of solitons are enhanced, which is essential for accurate modeling of nonlocal and dispersive effects in optical fibers. This work not only enhances fundamental understanding of nonlinear wave phenomena within optical communication systems but also offers valuable insights into using fractional calculus for designing and optimizing advanced photonic devices.https://www.aimspress.com/article/doi/10.3934/math.2025344nonlinear schrödinger equationsoliton solutionsfractional derivativesimproved modified extended tanh-function method |
| spellingShingle | Mahmoud Soliman Hamdy M. Ahmed Niveen Badra M. Elsaid Ramadan Islam Samir Soliman Alkhatib Influence of the $ \beta $-fractional derivative on optical soliton solutions of the pure-quartic nonlinear Schrödinger equation with weak nonlocality AIMS Mathematics nonlinear schrödinger equation soliton solutions fractional derivatives improved modified extended tanh-function method |
| title | Influence of the $ \beta $-fractional derivative on optical soliton solutions of the pure-quartic nonlinear Schrödinger equation with weak nonlocality |
| title_full | Influence of the $ \beta $-fractional derivative on optical soliton solutions of the pure-quartic nonlinear Schrödinger equation with weak nonlocality |
| title_fullStr | Influence of the $ \beta $-fractional derivative on optical soliton solutions of the pure-quartic nonlinear Schrödinger equation with weak nonlocality |
| title_full_unstemmed | Influence of the $ \beta $-fractional derivative on optical soliton solutions of the pure-quartic nonlinear Schrödinger equation with weak nonlocality |
| title_short | Influence of the $ \beta $-fractional derivative on optical soliton solutions of the pure-quartic nonlinear Schrödinger equation with weak nonlocality |
| title_sort | influence of the beta fractional derivative on optical soliton solutions of the pure quartic nonlinear schrodinger equation with weak nonlocality |
| topic | nonlinear schrödinger equation soliton solutions fractional derivatives improved modified extended tanh-function method |
| url | https://www.aimspress.com/article/doi/10.3934/math.2025344 |
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