Bifurcation analysis, chaotic behaviors, and explicit solutions for a fractional two-mode Nizhnik-Novikov-Veselov equation in mathematical physics
The two-mode Nizhnik-Novikov-Veselov (TMNNV) equation finds wide-ranging utility across engineering and scientific fields. It stands as a notable nonlinear physical model for explaining nonlinear soliton propagation. This study explores bifurcation analysis for the (2+1)-dimensional conformable time...
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AIMS Press
2025-03-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2025211 |
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| author | Noor Alam Mohammad Safi Ullah Jalil Manafian Khaled H. Mahmoud A. SA. Alsubaie Hamdy M. Ahmed Karim K. Ahmed Soliman Al Khatib |
| author_facet | Noor Alam Mohammad Safi Ullah Jalil Manafian Khaled H. Mahmoud A. SA. Alsubaie Hamdy M. Ahmed Karim K. Ahmed Soliman Al Khatib |
| author_sort | Noor Alam |
| collection | DOAJ |
| description | The two-mode Nizhnik-Novikov-Veselov (TMNNV) equation finds wide-ranging utility across engineering and scientific fields. It stands as a notable nonlinear physical model for explaining nonlinear soliton propagation. This study explores bifurcation analysis for the (2+1)-dimensional conformable time-fractional TMNNV model for the first time. Also, we have derived the explicit solutions of this model, and these solutions exhibit some unique dynamical patterns: combo bright-dark bell wave, periodic wave, bright soliton, and dark soliton, which are used in several optical applications. 2-D plots and combined 3-D with density plots are presented with the impacts of different parameters. Later, phase portraits and the multistability of this dynamical model are analyzed via intersecting figures with the help of the planner dynamical system. We also examine the quasi-periodic and chaotic behaviors of the governing model under different conditions. Finally, conclusions are drawn based on the results. |
| format | Article |
| id | doaj-art-2b1a99aff0734959ad294e8efc78e09b |
| institution | OA Journals |
| issn | 2473-6988 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-2b1a99aff0734959ad294e8efc78e09b2025-08-20T01:54:41ZengAIMS PressAIMS Mathematics2473-69882025-03-011034558457810.3934/math.2025211Bifurcation analysis, chaotic behaviors, and explicit solutions for a fractional two-mode Nizhnik-Novikov-Veselov equation in mathematical physicsNoor Alam0Mohammad Safi Ullah1Jalil Manafian2Khaled H. Mahmoud3A. SA. Alsubaie4Hamdy M. Ahmed5Karim K. Ahmed6Soliman Al Khatib7Department of Mathematics, Kishoreganj University, Kishoreganj 2300, BangladeshDepartment of Mathematics, Comilla University, Cumilla-3506, BangladeshDepartment of Applied Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, IranDepartment of Physics, College of Khurma University College, Taif University, Taif 21944, Saudi ArabiaDepartment of Physics, College of Khurma University College, Taif University, Taif 21944, Saudi ArabiaDepartment of Mathematics and Engineering Physics, Higher Institute of Engineering, El-Shorouk Academy, El-Shorouk City, Cairo, EgyptDepartment of Mathematics, Faculty of Engineering, German International University (GIU), New Administrative Capital, Cairo, EgyptCollege of Engineering and Technology, American University in the Emirates (AUE), Academic City, P.O. Box 503000, Dubai, UAEThe two-mode Nizhnik-Novikov-Veselov (TMNNV) equation finds wide-ranging utility across engineering and scientific fields. It stands as a notable nonlinear physical model for explaining nonlinear soliton propagation. This study explores bifurcation analysis for the (2+1)-dimensional conformable time-fractional TMNNV model for the first time. Also, we have derived the explicit solutions of this model, and these solutions exhibit some unique dynamical patterns: combo bright-dark bell wave, periodic wave, bright soliton, and dark soliton, which are used in several optical applications. 2-D plots and combined 3-D with density plots are presented with the impacts of different parameters. Later, phase portraits and the multistability of this dynamical model are analyzed via intersecting figures with the help of the planner dynamical system. We also examine the quasi-periodic and chaotic behaviors of the governing model under different conditions. Finally, conclusions are drawn based on the results.https://www.aimspress.com/article/doi/10.3934/math.2025211chaotic naturebifurcationphase portraitsmultistabilityequilibrium point |
| spellingShingle | Noor Alam Mohammad Safi Ullah Jalil Manafian Khaled H. Mahmoud A. SA. Alsubaie Hamdy M. Ahmed Karim K. Ahmed Soliman Al Khatib Bifurcation analysis, chaotic behaviors, and explicit solutions for a fractional two-mode Nizhnik-Novikov-Veselov equation in mathematical physics AIMS Mathematics chaotic nature bifurcation phase portraits multistability equilibrium point |
| title | Bifurcation analysis, chaotic behaviors, and explicit solutions for a fractional two-mode Nizhnik-Novikov-Veselov equation in mathematical physics |
| title_full | Bifurcation analysis, chaotic behaviors, and explicit solutions for a fractional two-mode Nizhnik-Novikov-Veselov equation in mathematical physics |
| title_fullStr | Bifurcation analysis, chaotic behaviors, and explicit solutions for a fractional two-mode Nizhnik-Novikov-Veselov equation in mathematical physics |
| title_full_unstemmed | Bifurcation analysis, chaotic behaviors, and explicit solutions for a fractional two-mode Nizhnik-Novikov-Veselov equation in mathematical physics |
| title_short | Bifurcation analysis, chaotic behaviors, and explicit solutions for a fractional two-mode Nizhnik-Novikov-Veselov equation in mathematical physics |
| title_sort | bifurcation analysis chaotic behaviors and explicit solutions for a fractional two mode nizhnik novikov veselov equation in mathematical physics |
| topic | chaotic nature bifurcation phase portraits multistability equilibrium point |
| url | https://www.aimspress.com/article/doi/10.3934/math.2025211 |
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