Exploring Nonlinear Dynamics and Solitary Waves in the Fractional Klein–Gordon Model
Various nonlinear evolution equations reveal the inner characteristics of numerous real-life complex phenomena. Using the extended fractional Riccati expansion method, we investigate optical soliton solutions of the fractional Klein–Gordon equation within this modified framework. This model in physi...
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| Main Authors: | , , , , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2025-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/admp/9970003 |
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| author | Md. Abde Mannaf Muktarebatul Jannah Md. Habibul Bashar Md. Ekramul Islam Md. Zuel Rana Mst. Tania Khatun Md. Noor-A-Alam Siddiki Md. Shahinur Islam |
| author_facet | Md. Abde Mannaf Muktarebatul Jannah Md. Habibul Bashar Md. Ekramul Islam Md. Zuel Rana Mst. Tania Khatun Md. Noor-A-Alam Siddiki Md. Shahinur Islam |
| author_sort | Md. Abde Mannaf |
| collection | DOAJ |
| description | Various nonlinear evolution equations reveal the inner characteristics of numerous real-life complex phenomena. Using the extended fractional Riccati expansion method, we investigate optical soliton solutions of the fractional Klein–Gordon equation within this modified framework. This model in physics claims the existence of energy particles and defines the relativistic wave. The proposed procedures provide insight into wave spread and optical solitons, which enterprises in current broadcast communications can utilize to empower fast and long-distance information transmission with minimal signal degradation. They are important for their reliability and optical communication networking. This method can analytically formulate optical soliton solutions using rational, hyperbolic, and trigonometric functions. The interaction between the breather and the king wave, as well as the bright and dark bell-shaped singular soliton waves, are the numerical forms of the obtained solutions, examined using three- and two-dimensional diagrams. These solutions are obtained using the proposed method. For [α, β = 0.1, 0.5, 0.9], we illustrate the impact of conformable and beta fractional parameters in two-dimensional graphs. Understanding and clarifying the physical characteristics of waves may be made easier by the collected results. Nonlinear optics, optical communications, and engineering all rely on unique and precise soliton solutions, and the aforementioned applied techniques may, therefore, serve as a valuable tool for this purpose. |
| format | Article |
| id | doaj-art-8767bfa762b548f1a20ea6668279e62e |
| institution | Kabale University |
| issn | 1687-9139 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-8767bfa762b548f1a20ea6668279e62e2025-08-20T03:41:57ZengWileyAdvances in Mathematical Physics1687-91392025-01-01202510.1155/admp/9970003Exploring Nonlinear Dynamics and Solitary Waves in the Fractional Klein–Gordon ModelMd. Abde Mannaf0Muktarebatul Jannah1Md. Habibul Bashar2Md. Ekramul Islam3Md. Zuel Rana4Mst. Tania Khatun5Md. Noor-A-Alam Siddiki6Md. Shahinur Islam7Department of MathematicsDepartment of MathematicsDepartment of Computer Science and EngineeringDepartment of MathematicsDepartment of PhysicsDepartment of MathematicsDepartment of Computer Science and EngineeringDepartment of Computer Science and EngineeringVarious nonlinear evolution equations reveal the inner characteristics of numerous real-life complex phenomena. Using the extended fractional Riccati expansion method, we investigate optical soliton solutions of the fractional Klein–Gordon equation within this modified framework. This model in physics claims the existence of energy particles and defines the relativistic wave. The proposed procedures provide insight into wave spread and optical solitons, which enterprises in current broadcast communications can utilize to empower fast and long-distance information transmission with minimal signal degradation. They are important for their reliability and optical communication networking. This method can analytically formulate optical soliton solutions using rational, hyperbolic, and trigonometric functions. The interaction between the breather and the king wave, as well as the bright and dark bell-shaped singular soliton waves, are the numerical forms of the obtained solutions, examined using three- and two-dimensional diagrams. These solutions are obtained using the proposed method. For [α, β = 0.1, 0.5, 0.9], we illustrate the impact of conformable and beta fractional parameters in two-dimensional graphs. Understanding and clarifying the physical characteristics of waves may be made easier by the collected results. Nonlinear optics, optical communications, and engineering all rely on unique and precise soliton solutions, and the aforementioned applied techniques may, therefore, serve as a valuable tool for this purpose.http://dx.doi.org/10.1155/admp/9970003 |
| spellingShingle | Md. Abde Mannaf Muktarebatul Jannah Md. Habibul Bashar Md. Ekramul Islam Md. Zuel Rana Mst. Tania Khatun Md. Noor-A-Alam Siddiki Md. Shahinur Islam Exploring Nonlinear Dynamics and Solitary Waves in the Fractional Klein–Gordon Model Advances in Mathematical Physics |
| title | Exploring Nonlinear Dynamics and Solitary Waves in the Fractional Klein–Gordon Model |
| title_full | Exploring Nonlinear Dynamics and Solitary Waves in the Fractional Klein–Gordon Model |
| title_fullStr | Exploring Nonlinear Dynamics and Solitary Waves in the Fractional Klein–Gordon Model |
| title_full_unstemmed | Exploring Nonlinear Dynamics and Solitary Waves in the Fractional Klein–Gordon Model |
| title_short | Exploring Nonlinear Dynamics and Solitary Waves in the Fractional Klein–Gordon Model |
| title_sort | exploring nonlinear dynamics and solitary waves in the fractional klein gordon model |
| url | http://dx.doi.org/10.1155/admp/9970003 |
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