Investigating higher dimensional Jimbo–Miwa nonlinear dynamics through phase portraits, sensitivity, chaos and soliton behavior
The main focus of this article is on the development of new wave structures for the nonlinear (3+1)-dimensional Jimbo–Miwa equation. To solve the Jimbo–Miwa equation, a modified Khater method has been employed to generate various forms of soliton wave structures. Exact solutions to this equation are...
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| Format: | Article |
| Language: | English |
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Elsevier
2025-03-01
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| Series: | Partial Differential Equations in Applied Mathematics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666818125000294 |
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| author | Muhammad Aziz ur Rehman Muhammad Bilal Riaz Muhammad Iqbal |
| author_facet | Muhammad Aziz ur Rehman Muhammad Bilal Riaz Muhammad Iqbal |
| author_sort | Muhammad Aziz ur Rehman |
| collection | DOAJ |
| description | The main focus of this article is on the development of new wave structures for the nonlinear (3+1)-dimensional Jimbo–Miwa equation. To solve the Jimbo–Miwa equation, a modified Khater method has been employed to generate various forms of soliton wave structures. Exact solutions to this equation are considered important for the complete understanding of the dynamics of waves in a physical model. The dynamic behavior of wave structures, including solutions for brilliant, single, dark, and periodic singular solitons, is enlightened by the obtained results. Selected solutions are plotted in both two- and three-dimensional graphs to illustrate their behavior. Furthermore, the system is converted into a planar dynamical system, and the derived solutions are examined using phase portraits to illustrate and demonstrate the theoretical results. Bifurcation and chaos theories are applied to enhance comprehension of the planar dynamical system that emerges from the examined system. Additionally, an investigation into the sensitivity of the provided model is conducted, revealing a moderate level of sensitivity and stability. These innovative concepts are utilized through symbolic computations to provide comprehensive and powerful mathematical tools for addressing various benign nonlinear problems. |
| format | Article |
| id | doaj-art-c2652e7c97ce4f5f9bcbcdeb306223ec |
| institution | Kabale University |
| issn | 2666-8181 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Partial Differential Equations in Applied Mathematics |
| spelling | doaj-art-c2652e7c97ce4f5f9bcbcdeb306223ec2025-02-06T05:12:57ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812025-03-0113101101Investigating higher dimensional Jimbo–Miwa nonlinear dynamics through phase portraits, sensitivity, chaos and soliton behaviorMuhammad Aziz ur Rehman0Muhammad Bilal Riaz1Muhammad Iqbal2Department of Mathematics, University of Management and Technology, Lahore, Pakistan; Corresponding author.IT4Innovations, VSB – Technical University of Ostrava, Ostrava, Czech Republic; Department of Computer Science and Mathematics, Lebanese American University, Byblos, LebanonDepartment of Mathematics, University of Management and Technology, Lahore, PakistanThe main focus of this article is on the development of new wave structures for the nonlinear (3+1)-dimensional Jimbo–Miwa equation. To solve the Jimbo–Miwa equation, a modified Khater method has been employed to generate various forms of soliton wave structures. Exact solutions to this equation are considered important for the complete understanding of the dynamics of waves in a physical model. The dynamic behavior of wave structures, including solutions for brilliant, single, dark, and periodic singular solitons, is enlightened by the obtained results. Selected solutions are plotted in both two- and three-dimensional graphs to illustrate their behavior. Furthermore, the system is converted into a planar dynamical system, and the derived solutions are examined using phase portraits to illustrate and demonstrate the theoretical results. Bifurcation and chaos theories are applied to enhance comprehension of the planar dynamical system that emerges from the examined system. Additionally, an investigation into the sensitivity of the provided model is conducted, revealing a moderate level of sensitivity and stability. These innovative concepts are utilized through symbolic computations to provide comprehensive and powerful mathematical tools for addressing various benign nonlinear problems.http://www.sciencedirect.com/science/article/pii/S2666818125000294Jimbo–Miwa equationExact solutionsDynamical systemModified Khater method |
| spellingShingle | Muhammad Aziz ur Rehman Muhammad Bilal Riaz Muhammad Iqbal Investigating higher dimensional Jimbo–Miwa nonlinear dynamics through phase portraits, sensitivity, chaos and soliton behavior Partial Differential Equations in Applied Mathematics Jimbo–Miwa equation Exact solutions Dynamical system Modified Khater method |
| title | Investigating higher dimensional Jimbo–Miwa nonlinear dynamics through phase portraits, sensitivity, chaos and soliton behavior |
| title_full | Investigating higher dimensional Jimbo–Miwa nonlinear dynamics through phase portraits, sensitivity, chaos and soliton behavior |
| title_fullStr | Investigating higher dimensional Jimbo–Miwa nonlinear dynamics through phase portraits, sensitivity, chaos and soliton behavior |
| title_full_unstemmed | Investigating higher dimensional Jimbo–Miwa nonlinear dynamics through phase portraits, sensitivity, chaos and soliton behavior |
| title_short | Investigating higher dimensional Jimbo–Miwa nonlinear dynamics through phase portraits, sensitivity, chaos and soliton behavior |
| title_sort | investigating higher dimensional jimbo miwa nonlinear dynamics through phase portraits sensitivity chaos and soliton behavior |
| topic | Jimbo–Miwa equation Exact solutions Dynamical system Modified Khater method |
| url | http://www.sciencedirect.com/science/article/pii/S2666818125000294 |
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