Bifurcations, chaotic behavior, and optical solutions for the complex Ginzburg–Landau equation
This research focuses on investigating an extended version of the Ginzburg–Landau (GL) equation that describes the motion of particles in a plasma. The other applications of this model can be found in optics, and other related fields. As part of our approach, we seek to discover some new wave soluti...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2024-04-01
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| Series: | Results in Physics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2211379724002845 |
| _version_ | 1797213416627109888 |
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| author | C. Zhu M. Al-Dossari S. Rezapour S.A.M. Alsallami B. Gunay |
| author_facet | C. Zhu M. Al-Dossari S. Rezapour S.A.M. Alsallami B. Gunay |
| author_sort | C. Zhu |
| collection | DOAJ |
| description | This research focuses on investigating an extended version of the Ginzburg–Landau (GL) equation that describes the motion of particles in a plasma. The other applications of this model can be found in optics, and other related fields. As part of our approach, we seek to discover some new wave solutions to the model, and then use the Galilean transformation in order to determine the model’s dynamical properties. After that, we use planar dynamical system theory to perform an in-depth bifurcation analysis, which gives us valuable insight into the system. By conducting thorough mathematical and bifurcation analyses, we identify the fundamental dynamics and critical points that regulate the system’s behavior. Moreover we explore the chaotic nature of the system, uncovering potential chaotic tendencies and their consequences. Further, we obtain several categories of optical solutions of the complex GL equation by utilizing new logarithmic transformations, offering valuable insight into its behavior and potential applications in optics. Our analytical technique yields closed-form solutions expressing elementary functions. In order to ensure the reliability of our findings, we rigorously validate the obtained solutions by substituting them back into the original model. Our research helps us better understand this equation’s characteristics and its relevance across a wide range of disciplines. |
| first_indexed | 2024-04-24T10:57:56Z |
| format | Article |
| id | doaj.art-da81ef6e7e874cd39a1579533da61a60 |
| institution | Directory Open Access Journal |
| issn | 2211-3797 |
| language | English |
| last_indexed | 2024-04-24T10:57:56Z |
| publishDate | 2024-04-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Physics |
| spelling | doaj.art-da81ef6e7e874cd39a1579533da61a602024-04-12T04:45:17ZengElsevierResults in Physics2211-37972024-04-0159107601Bifurcations, chaotic behavior, and optical solutions for the complex Ginzburg–Landau equationC. Zhu0M. Al-Dossari1S. Rezapour2S.A.M. Alsallami3B. Gunay4Institute of Social Innovation and Public Culture, Communication University of China, Beijing, 100024, China; Corresponding authors.Department of Physics, Faculty of Science, King Khalid University, Abha 62529, Saudi ArabiaDepartment of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran; Insurance Research Center (IRC), Tehran, Iran; Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan; Corresponding authors.Mathematics Department, College of Sciences, Umm Al-Qura University, Makkah 24381, Saudi ArabiaFaculty of Engineering and Natural Sciences, Bahçeşehir University, 34349 Istanbul, TurkeyThis research focuses on investigating an extended version of the Ginzburg–Landau (GL) equation that describes the motion of particles in a plasma. The other applications of this model can be found in optics, and other related fields. As part of our approach, we seek to discover some new wave solutions to the model, and then use the Galilean transformation in order to determine the model’s dynamical properties. After that, we use planar dynamical system theory to perform an in-depth bifurcation analysis, which gives us valuable insight into the system. By conducting thorough mathematical and bifurcation analyses, we identify the fundamental dynamics and critical points that regulate the system’s behavior. Moreover we explore the chaotic nature of the system, uncovering potential chaotic tendencies and their consequences. Further, we obtain several categories of optical solutions of the complex GL equation by utilizing new logarithmic transformations, offering valuable insight into its behavior and potential applications in optics. Our analytical technique yields closed-form solutions expressing elementary functions. In order to ensure the reliability of our findings, we rigorously validate the obtained solutions by substituting them back into the original model. Our research helps us better understand this equation’s characteristics and its relevance across a wide range of disciplines.http://www.sciencedirect.com/science/article/pii/S2211379724002845Bifurcation analysisThe Ginzburg–Landau equationChaotic behaviorsThe Galilean transformationSolitons solutionsNumerical calculations |
| spellingShingle | C. Zhu M. Al-Dossari S. Rezapour S.A.M. Alsallami B. Gunay Bifurcations, chaotic behavior, and optical solutions for the complex Ginzburg–Landau equation Results in Physics Bifurcation analysis The Ginzburg–Landau equation Chaotic behaviors The Galilean transformation Solitons solutions Numerical calculations |
| title | Bifurcations, chaotic behavior, and optical solutions for the complex Ginzburg–Landau equation |
| title_full | Bifurcations, chaotic behavior, and optical solutions for the complex Ginzburg–Landau equation |
| title_fullStr | Bifurcations, chaotic behavior, and optical solutions for the complex Ginzburg–Landau equation |
| title_full_unstemmed | Bifurcations, chaotic behavior, and optical solutions for the complex Ginzburg–Landau equation |
| title_short | Bifurcations, chaotic behavior, and optical solutions for the complex Ginzburg–Landau equation |
| title_sort | bifurcations chaotic behavior and optical solutions for the complex ginzburg landau equation |
| topic | Bifurcation analysis The Ginzburg–Landau equation Chaotic behaviors The Galilean transformation Solitons solutions Numerical calculations |
| url | http://www.sciencedirect.com/science/article/pii/S2211379724002845 |
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