Soliton structures and dynamical behaviors for the integrable system of Drinfel’d–Sokolov–Wilson equations in dispersive media
This study is used to investigate the exact explicit solutions and dynamical behaviors of the (1+1)-dimensional integrable system of Drinfel’d–Sokolov–Wilson equations in dispersive media. Firstly, the unified method is implemented to find explicit solutions in polynomial and rational forms. These s...
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| Format: | Article |
| Language: | English |
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Elsevier
2023-03-01
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| Series: | Results in Physics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2211379723000621 |
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| author | Haifa I. Alrebdi Muhammad Hamza Rafiq Nahid Fatima Nauman Raza Muhammad Naveed Rafiq B. Alshahrani Abdel-Haleem Abdel-Aty |
| author_facet | Haifa I. Alrebdi Muhammad Hamza Rafiq Nahid Fatima Nauman Raza Muhammad Naveed Rafiq B. Alshahrani Abdel-Haleem Abdel-Aty |
| author_sort | Haifa I. Alrebdi |
| collection | DOAJ |
| description | This study is used to investigate the exact explicit solutions and dynamical behaviors of the (1+1)-dimensional integrable system of Drinfel’d–Sokolov–Wilson equations in dispersive media. Firstly, the unified method is implemented to find explicit solutions in polynomial and rational forms. These solutions include rational, dark and bright soliton structures. After that, the planar dynamical system of the considered model is obtained using the Galilean transformation. The phase portraits of the bifurcations are drawn from the planar dynamical system for different physical parametric values using the fourth-order Runge–Kutta method. Further, an external force is imposed on the dynamical system to observe the phase portraits of chaotic trajectories. These tracks are outlined for different values of the strength and frequency of the external force acting on the dynamical system. The outcomes show that a given model has chaotic behvior as its solution becomes disordered by taking small variation in the strength and frequency of the external force. The results are new and can be helpful in investigating the dynamical behaviors of the other nonlinear physical models arising in optics, bio-mathematics and so many other fields of science. |
| first_indexed | 2024-04-10T00:30:18Z |
| format | Article |
| id | doaj.art-d8e9eb77794145ffaf2d1bbbf196c9cb |
| institution | Directory Open Access Journal |
| issn | 2211-3797 |
| language | English |
| last_indexed | 2024-04-10T00:30:18Z |
| publishDate | 2023-03-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Physics |
| spelling | doaj.art-d8e9eb77794145ffaf2d1bbbf196c9cb2023-03-15T04:27:44ZengElsevierResults in Physics2211-37972023-03-0146106269Soliton structures and dynamical behaviors for the integrable system of Drinfel’d–Sokolov–Wilson equations in dispersive mediaHaifa I. Alrebdi0Muhammad Hamza Rafiq1Nahid Fatima2Nauman Raza3Muhammad Naveed Rafiq4B. Alshahrani5Abdel-Haleem Abdel-Aty6Department of Physics, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi ArabiaDepartment of Mathematics and Statistics, The University of Lahore, Lahore 54000, PakistanDepartment of Mathematics & Sciences, Prince Sultan University, Riyadh 11586, Saudi ArabiaDepartment of Mathematics, University of the Punjab, Quaid-e-Azam Campus, Lahore 54590, PakistanSchool of Mathematics and Statistics, Central South University, Changsha 410083, ChinaDepartment of Physics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi ArabiaDepartment of Physics, College of Sciences, University of Bisha, PO Box 344, Bisha 61922, Saudi Arabia; Physics Department, Faculty of Science, Al-Azhar University, Assiut 71524, Egypt; Corresponding author at: Department of Physics, College of Sciences, University of Bisha, PO Box 344, Bisha 61922, Saudi Arabia.This study is used to investigate the exact explicit solutions and dynamical behaviors of the (1+1)-dimensional integrable system of Drinfel’d–Sokolov–Wilson equations in dispersive media. Firstly, the unified method is implemented to find explicit solutions in polynomial and rational forms. These solutions include rational, dark and bright soliton structures. After that, the planar dynamical system of the considered model is obtained using the Galilean transformation. The phase portraits of the bifurcations are drawn from the planar dynamical system for different physical parametric values using the fourth-order Runge–Kutta method. Further, an external force is imposed on the dynamical system to observe the phase portraits of chaotic trajectories. These tracks are outlined for different values of the strength and frequency of the external force acting on the dynamical system. The outcomes show that a given model has chaotic behvior as its solution becomes disordered by taking small variation in the strength and frequency of the external force. The results are new and can be helpful in investigating the dynamical behaviors of the other nonlinear physical models arising in optics, bio-mathematics and so many other fields of science.http://www.sciencedirect.com/science/article/pii/S2211379723000621Soliton structuresDynamical systemPhase portraits of bifurcation and chaotic behaviorsThe unified methodIntegrable system of Drinfel’d–Sokolov–Wilson equations |
| spellingShingle | Haifa I. Alrebdi Muhammad Hamza Rafiq Nahid Fatima Nauman Raza Muhammad Naveed Rafiq B. Alshahrani Abdel-Haleem Abdel-Aty Soliton structures and dynamical behaviors for the integrable system of Drinfel’d–Sokolov–Wilson equations in dispersive media Results in Physics Soliton structures Dynamical system Phase portraits of bifurcation and chaotic behaviors The unified method Integrable system of Drinfel’d–Sokolov–Wilson equations |
| title | Soliton structures and dynamical behaviors for the integrable system of Drinfel’d–Sokolov–Wilson equations in dispersive media |
| title_full | Soliton structures and dynamical behaviors for the integrable system of Drinfel’d–Sokolov–Wilson equations in dispersive media |
| title_fullStr | Soliton structures and dynamical behaviors for the integrable system of Drinfel’d–Sokolov–Wilson equations in dispersive media |
| title_full_unstemmed | Soliton structures and dynamical behaviors for the integrable system of Drinfel’d–Sokolov–Wilson equations in dispersive media |
| title_short | Soliton structures and dynamical behaviors for the integrable system of Drinfel’d–Sokolov–Wilson equations in dispersive media |
| title_sort | soliton structures and dynamical behaviors for the integrable system of drinfel d sokolov wilson equations in dispersive media |
| topic | Soliton structures Dynamical system Phase portraits of bifurcation and chaotic behaviors The unified method Integrable system of Drinfel’d–Sokolov–Wilson equations |
| url | http://www.sciencedirect.com/science/article/pii/S2211379723000621 |
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