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2025, Volume 10, Issue 3: 4558-4578. doi: 10.3934/math.2025211
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Bifurcation analysis, chaotic behaviors, and explicit solutions for a fractional two-mode Nizhnik-Novikov-Veselov equation in mathematical physics

  • 1.
    Department of Mathematics, Kishoreganj University, Kishoreganj 2300, Bangladesh
  • 2.
    Department of Mathematics, Comilla University, Cumilla-3506, Bangladesh
  • 3.
    Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran
  • 4.
    Natural Sciences Faculty, Lankaran State University, H. Aslanov str., Lankaran, Azerbaijan
  • 5.
    Department of Physics, College of Khurma University College, Taif University, Taif 21944, Saudi Arabia
  • 6.
    Department of Mathematics and Engineering Physics, Higher Institute of Engineering, El-Shorouk Academy, El-Shorouk City, Cairo, Egypt
  • 7.
    Department of Mathematics, Faculty of Engineering, German International University (GIU), New Administrative Capital, Cairo, Egypt
  • 8.
    College of Engineering and Technology, American University in the Emirates (AUE), Academic City, P.O. Box 503000, Dubai, UAE
  • Received: 13 September 2024 Revised: 11 December 2024 Accepted: 23 December 2024 Published: 03 March 2025

  • MSC : 35C08, 74J35

  • 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.

    Citation: 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[J]. AIMS Mathematics, 2025, 10(3): 4558-4578. doi: 10.3934/math.2025211

    Related Papers:

  • 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.



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