Chaotic behavior and construction of a variety of wave structures related to a new form of generalized q-Deformed sinh-Gordon model using couple of integration norms
The generalized q-deformed sinh Gordon equation (GDSGE) serves as a significant nonlinear partial differential equation with profound applications in physics. This study investigates the GDSGE's mathematical and physical properties, examining its solutions and clarifying the essence of the q-de...
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AIMS Press
2024-03-01
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| Online Access: | https://aimspress.com/article/doi/10.3934/math.2024466?viewType=HTML |
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| author | Wedad Albalawi Nauman Raza Saima Arshed Muhammad Farman Kottakkaran Sooppy Nisar Abdel-Haleem Abdel-Aty |
| author_facet | Wedad Albalawi Nauman Raza Saima Arshed Muhammad Farman Kottakkaran Sooppy Nisar Abdel-Haleem Abdel-Aty |
| author_sort | Wedad Albalawi |
| collection | DOAJ |
| description | The generalized q-deformed sinh Gordon equation (GDSGE) serves as a significant nonlinear partial differential equation with profound applications in physics. This study investigates the GDSGE's mathematical and physical properties, examining its solutions and clarifying the essence of the q-deformation parameter. The Sardar sub-equation method (SSEM) and sine-Gordon expansion method (SGEM) are employed to solve this GDSGE. The synergistic application of these techniques improves our knowledge of the GDSGE and provides a thorough foundation for investigating different evolution models arising in various branches of mathematics and physics. A positive aspect of the proposed methods is that they offer a wide variety of solitons, including bright, singular, dark, combination dark-singular, combined dark-bright, and periodic singular solitons. Obtained solutions demonstrate the method's high degree of reliability, simplicity, and functionalization for various nonlinear equations. To better describe the physical characterization of solutions, a few 2D and 3D visualizations are generated by taking precise values for parameters using mathematical software, Mathematica. |
| first_indexed | 2024-04-24T21:45:15Z |
| format | Article |
| id | doaj.art-ee8cc6cc357c4629a0814b9c666b20b4 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-24T21:45:15Z |
| publishDate | 2024-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-ee8cc6cc357c4629a0814b9c666b20b42024-03-21T01:17:14ZengAIMS PressAIMS Mathematics2473-69882024-03-01949536955510.3934/math.2024466Chaotic behavior and construction of a variety of wave structures related to a new form of generalized q-Deformed sinh-Gordon model using couple of integration normsWedad Albalawi0Nauman Raza 1 Saima Arshed 2Muhammad Farman 3Kottakkaran Sooppy Nisar 4Abdel-Haleem Abdel-Aty51. Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia2. Department of Mathematics, University of the Punjab, Quaid-e-Azam Campus, Lahore 54590, Pakistan4. Faculty of Arts and Science, Department of Mathematics, Near East University, Cyprus, Turkey2. Department of Mathematics, University of the Punjab, Quaid-e-Azam Campus, Lahore 54590, Pakistan3. Department of Computer Science and Mathematics, Lebanese American University, 1107-2020, Beirut, Lebanon 4. Faculty of Arts and Science, Department of Mathematics, Near East University, Cyprus, Turkey5. Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam Bin Abdulaziz University, Alkharj 11942, Saudi Arabia6. Department of Physics, College of Sciences, University of Bisha, Bisha 61922, Saudi ArabiaThe generalized q-deformed sinh Gordon equation (GDSGE) serves as a significant nonlinear partial differential equation with profound applications in physics. This study investigates the GDSGE's mathematical and physical properties, examining its solutions and clarifying the essence of the q-deformation parameter. The Sardar sub-equation method (SSEM) and sine-Gordon expansion method (SGEM) are employed to solve this GDSGE. The synergistic application of these techniques improves our knowledge of the GDSGE and provides a thorough foundation for investigating different evolution models arising in various branches of mathematics and physics. A positive aspect of the proposed methods is that they offer a wide variety of solitons, including bright, singular, dark, combination dark-singular, combined dark-bright, and periodic singular solitons. Obtained solutions demonstrate the method's high degree of reliability, simplicity, and functionalization for various nonlinear equations. To better describe the physical characterization of solutions, a few 2D and 3D visualizations are generated by taking precise values for parameters using mathematical software, Mathematica.https://aimspress.com/article/doi/10.3934/math.2024466?viewType=HTMLgeneralized q-deformed sinh gordon equationsardar sub-equation methodsine-gordon expansion methodsolitons |
| spellingShingle | Wedad Albalawi Nauman Raza Saima Arshed Muhammad Farman Kottakkaran Sooppy Nisar Abdel-Haleem Abdel-Aty Chaotic behavior and construction of a variety of wave structures related to a new form of generalized q-Deformed sinh-Gordon model using couple of integration norms AIMS Mathematics generalized q-deformed sinh gordon equation sardar sub-equation method sine-gordon expansion method solitons |
| title | Chaotic behavior and construction of a variety of wave structures related to a new form of generalized q-Deformed sinh-Gordon model using couple of integration norms |
| title_full | Chaotic behavior and construction of a variety of wave structures related to a new form of generalized q-Deformed sinh-Gordon model using couple of integration norms |
| title_fullStr | Chaotic behavior and construction of a variety of wave structures related to a new form of generalized q-Deformed sinh-Gordon model using couple of integration norms |
| title_full_unstemmed | Chaotic behavior and construction of a variety of wave structures related to a new form of generalized q-Deformed sinh-Gordon model using couple of integration norms |
| title_short | Chaotic behavior and construction of a variety of wave structures related to a new form of generalized q-Deformed sinh-Gordon model using couple of integration norms |
| title_sort | chaotic behavior and construction of a variety of wave structures related to a new form of generalized q deformed sinh gordon model using couple of integration norms |
| topic | generalized q-deformed sinh gordon equation sardar sub-equation method sine-gordon expansion method solitons |
| url | https://aimspress.com/article/doi/10.3934/math.2024466?viewType=HTML |
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