Optical wave patterns and chaotic dynamics of the variable coefficient fractional nonlinear Schrödinger equation: Analytical and numerical insights
This study looks into the variable coefficient third-order nonlinear Schrödinger equation (NLSE) with truncated M-fractional derivative in a methodical way. It focuses on chaotic dynamics, sensitivity analysis, and optical soliton solutions. The NLSE serves as a fundamental model in nonlinear optics...
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Elsevier
2025-09-01
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| Series: | Results in Engineering |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2590123025018195 |
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| author | Mahtab Uddin Mohammed Kbiri Alaoui Md. Mamunur Roshid Golam Mostafa Harun-Or-Roshid |
| author_facet | Mahtab Uddin Mohammed Kbiri Alaoui Md. Mamunur Roshid Golam Mostafa Harun-Or-Roshid |
| author_sort | Mahtab Uddin |
| collection | DOAJ |
| description | This study looks into the variable coefficient third-order nonlinear Schrödinger equation (NLSE) with truncated M-fractional derivative in a methodical way. It focuses on chaotic dynamics, sensitivity analysis, and optical soliton solutions. The NLSE serves as a fundamental model in nonlinear optics, quantum physics, and plasma dynamics, making this study particularly relevant for modern physics applications. We look at the system's chaotic behavior under certain parameter conditions and also investigate the Lyapunov exponent map. The numerical results are shown in the form of phase portraits. The sensitivity analysis reveals how small parameter perturbations significantly affect system stability, demonstrating the model's delicate balance. For optical soliton solutions, we employ two robust analytical methods: the newly modified Kudryashov (NMK) technique and the extended modified F-expansion (EMFE) approach. The NMK method yields various wave patterns, including hyperbolic breathers, kink solitons, rogue waves, and shock solutions. The EMFE method generates additional solutions like dark solitons, multi-breather waves, and double periodic structures. These solutions are visualized through 3D surface plots, density diagrams, and 2D representations. The study particularly examines the impact of the fractional parameter γ(0.1,0.5,0.9) on wave propagation characteristics. Comparative 2D plots demonstrate how γ influences solution behavior, with lower values showing more pronounced fractional effects. The analysis confirms both methods effectively capture the rich solution space of the fractional NLSE. These findings advance our understanding of nonlinear wave propagation in fractional systems and provide valuable tools for optical communication design. The derived solutions offer potential applications in soliton-based signal processing and nonlinear photonic devices. |
| format | Article |
| id | doaj-art-c58b556b488c4e59b1cdd25f033e26a7 |
| institution | Kabale University |
| issn | 2590-1230 |
| language | English |
| publishDate | 2025-09-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Engineering |
| spelling | doaj-art-c58b556b488c4e59b1cdd25f033e26a72025-08-20T03:32:46ZengElsevierResults in Engineering2590-12302025-09-012710574810.1016/j.rineng.2025.105748Optical wave patterns and chaotic dynamics of the variable coefficient fractional nonlinear Schrödinger equation: Analytical and numerical insightsMahtab Uddin0Mohammed Kbiri Alaoui1Md. Mamunur Roshid2Golam Mostafa3 Harun-Or-Roshid4Institute of Natural Sciences, United International University, Dhaka-1212, BangladeshDepartment of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha, 61413, Saudi ArabiaDepartment of Mathematics, Hamdard University Bangladesh, Munshiganj-1510, BangladeshDepartment of Computer Science and Engineering, Southeast University, Dhaka-1208, Bangladesh; Corresponding author.Department of Mathematics, Sunamgonj University of Science and Technology, Sunamganj-3000, BangladeshThis study looks into the variable coefficient third-order nonlinear Schrödinger equation (NLSE) with truncated M-fractional derivative in a methodical way. It focuses on chaotic dynamics, sensitivity analysis, and optical soliton solutions. The NLSE serves as a fundamental model in nonlinear optics, quantum physics, and plasma dynamics, making this study particularly relevant for modern physics applications. We look at the system's chaotic behavior under certain parameter conditions and also investigate the Lyapunov exponent map. The numerical results are shown in the form of phase portraits. The sensitivity analysis reveals how small parameter perturbations significantly affect system stability, demonstrating the model's delicate balance. For optical soliton solutions, we employ two robust analytical methods: the newly modified Kudryashov (NMK) technique and the extended modified F-expansion (EMFE) approach. The NMK method yields various wave patterns, including hyperbolic breathers, kink solitons, rogue waves, and shock solutions. The EMFE method generates additional solutions like dark solitons, multi-breather waves, and double periodic structures. These solutions are visualized through 3D surface plots, density diagrams, and 2D representations. The study particularly examines the impact of the fractional parameter γ(0.1,0.5,0.9) on wave propagation characteristics. Comparative 2D plots demonstrate how γ influences solution behavior, with lower values showing more pronounced fractional effects. The analysis confirms both methods effectively capture the rich solution space of the fractional NLSE. These findings advance our understanding of nonlinear wave propagation in fractional systems and provide valuable tools for optical communication design. The derived solutions offer potential applications in soliton-based signal processing and nonlinear photonic devices.http://www.sciencedirect.com/science/article/pii/S2590123025018195Nonlinear schrödinger’s equationChaotic natureTelecommunication systemsOptical communicationsIndustry, innovation, and infrastructure |
| spellingShingle | Mahtab Uddin Mohammed Kbiri Alaoui Md. Mamunur Roshid Golam Mostafa Harun-Or-Roshid Optical wave patterns and chaotic dynamics of the variable coefficient fractional nonlinear Schrödinger equation: Analytical and numerical insights Results in Engineering Nonlinear schrödinger’s equation Chaotic nature Telecommunication systems Optical communications Industry, innovation, and infrastructure |
| title | Optical wave patterns and chaotic dynamics of the variable coefficient fractional nonlinear Schrödinger equation: Analytical and numerical insights |
| title_full | Optical wave patterns and chaotic dynamics of the variable coefficient fractional nonlinear Schrödinger equation: Analytical and numerical insights |
| title_fullStr | Optical wave patterns and chaotic dynamics of the variable coefficient fractional nonlinear Schrödinger equation: Analytical and numerical insights |
| title_full_unstemmed | Optical wave patterns and chaotic dynamics of the variable coefficient fractional nonlinear Schrödinger equation: Analytical and numerical insights |
| title_short | Optical wave patterns and chaotic dynamics of the variable coefficient fractional nonlinear Schrödinger equation: Analytical and numerical insights |
| title_sort | optical wave patterns and chaotic dynamics of the variable coefficient fractional nonlinear schrodinger equation analytical and numerical insights |
| topic | Nonlinear schrödinger’s equation Chaotic nature Telecommunication systems Optical communications Industry, innovation, and infrastructure |
| url | http://www.sciencedirect.com/science/article/pii/S2590123025018195 |
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