Analytical and numerical investigation of soliton wave solutions in the fifth-order KdV equation within the KdV-KP framework
This study investigates the fifth-order Korteweg–de Vries (fKdV) equation, which is a generalized form of the classical KdV equation governing weakly nonlinear waves in dispersive media. By employing analytical and numerical techniques, the Khater II and variational iteration methods are utilized to...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2023-08-01
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| Series: | Results in Physics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2211379723004394 |
| _version_ | 1797755006028349440 |
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| author | Raghda A.M. Attia Youbing Xia Xiao Zhang Mostafa M.A. Khater |
| author_facet | Raghda A.M. Attia Youbing Xia Xiao Zhang Mostafa M.A. Khater |
| author_sort | Raghda A.M. Attia |
| collection | DOAJ |
| description | This study investigates the fifth-order Korteweg–de Vries (fKdV) equation, which is a generalized form of the classical KdV equation governing weakly nonlinear waves in dispersive media. By employing analytical and numerical techniques, the Khater II and variational iteration methods are utilized to obtain accurate soliton wave solutions. The combination of these approaches ensures the reliability and precision of the analytical outcomes. Graphical representations, including two-dimensional, three-dimensional, and contour plots, visually illustrate the results. Additionally, the stability of the constructed solutions is assessed through the characterization of the Hamiltonian system, providing valuable insights into the soliton wave solutions’ stability properties. This research integrates analytical and numerical methods to explore the fKdV equation within the KdV-KP framework, offering novel soliton wave solutions and enhancing their interpretation through graphical representations while assessing their stability using the Hamiltonian system’s characterization. |
| first_indexed | 2024-03-12T17:41:41Z |
| format | Article |
| id | doaj.art-6fe8508b7af44f5eb1a0b505adc17cf5 |
| institution | Directory Open Access Journal |
| issn | 2211-3797 |
| language | English |
| last_indexed | 2024-03-12T17:41:41Z |
| publishDate | 2023-08-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Physics |
| spelling | doaj.art-6fe8508b7af44f5eb1a0b505adc17cf52023-08-04T05:47:07ZengElsevierResults in Physics2211-37972023-08-0151106646Analytical and numerical investigation of soliton wave solutions in the fifth-order KdV equation within the KdV-KP frameworkRaghda A.M. Attia0Youbing Xia1Xiao Zhang2Mostafa M.A. Khater3School of Medical Informatics and Engineering, Xuzhou Medical University, 209 Tongshan Road, 221004, Xuzhou, Jiangsu Province, PR China; Department of Basic Science, Higher Technological Institute 10th of Ramadan City, El Sharqia 44634, EgyptSchool of Medical Informatics and Engineering, Xuzhou Medical University, 209 Tongshan Road, 221004, Xuzhou, Jiangsu Province, PR China; Key Laboratory of Acupuncture and Medicine Research of Ministry of Education, Nanjing University of Chinese Medicine, Nanjing, 210023, PR ChinaSchool of Medical Informatics and Engineering, Xuzhou Medical University, 209 Tongshan Road, 221004, Xuzhou, Jiangsu Province, PR ChinaSchool of Medical Informatics and Engineering, Xuzhou Medical University, 209 Tongshan Road, 221004, Xuzhou, Jiangsu Province, PR China; Department of Basic Science, Obour High Institute for Engineering and Technology, 11828, Cairo, Egypt; Corresponding author at: School of Medical Informatics and Engineering, Xuzhou Medical University, 209 Tongshan Road, 221004, Xuzhou, Jiangsu Province, PR China.This study investigates the fifth-order Korteweg–de Vries (fKdV) equation, which is a generalized form of the classical KdV equation governing weakly nonlinear waves in dispersive media. By employing analytical and numerical techniques, the Khater II and variational iteration methods are utilized to obtain accurate soliton wave solutions. The combination of these approaches ensures the reliability and precision of the analytical outcomes. Graphical representations, including two-dimensional, three-dimensional, and contour plots, visually illustrate the results. Additionally, the stability of the constructed solutions is assessed through the characterization of the Hamiltonian system, providing valuable insights into the soliton wave solutions’ stability properties. This research integrates analytical and numerical methods to explore the fKdV equation within the KdV-KP framework, offering novel soliton wave solutions and enhancing their interpretation through graphical representations while assessing their stability using the Hamiltonian system’s characterization.http://www.sciencedirect.com/science/article/pii/S2211379723004394Korteweg–de Vries–Kadomtsev–Petviashvili equationFifth-order Korteweg-de Vries equationSoliton wave solutionsAnalytical and numerical techniquesStability |
| spellingShingle | Raghda A.M. Attia Youbing Xia Xiao Zhang Mostafa M.A. Khater Analytical and numerical investigation of soliton wave solutions in the fifth-order KdV equation within the KdV-KP framework Results in Physics Korteweg–de Vries–Kadomtsev–Petviashvili equation Fifth-order Korteweg-de Vries equation Soliton wave solutions Analytical and numerical techniques Stability |
| title | Analytical and numerical investigation of soliton wave solutions in the fifth-order KdV equation within the KdV-KP framework |
| title_full | Analytical and numerical investigation of soliton wave solutions in the fifth-order KdV equation within the KdV-KP framework |
| title_fullStr | Analytical and numerical investigation of soliton wave solutions in the fifth-order KdV equation within the KdV-KP framework |
| title_full_unstemmed | Analytical and numerical investigation of soliton wave solutions in the fifth-order KdV equation within the KdV-KP framework |
| title_short | Analytical and numerical investigation of soliton wave solutions in the fifth-order KdV equation within the KdV-KP framework |
| title_sort | analytical and numerical investigation of soliton wave solutions in the fifth order kdv equation within the kdv kp framework |
| topic | Korteweg–de Vries–Kadomtsev–Petviashvili equation Fifth-order Korteweg-de Vries equation Soliton wave solutions Analytical and numerical techniques Stability |
| url | http://www.sciencedirect.com/science/article/pii/S2211379723004394 |
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