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Complex behaviors and various soliton profiles of (2+1)-dimensional complex modified Korteweg-de-Vries Equation

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Abstract

Nonlinear dynamical problems, characterized by unpredictable and chaotic changes among variables over time, pose unique challenges in understanding. This paper explores the coupled nonlinear (2+1)-dimensional complex modified Korteweg-de-Vries (cmKdV) equation-a fundamental equation in applied magnetism and nanophysics. The study focuses on dynamic behaviors, specifically examining bifurcations and equilibrium points leading to chaotic phenomena by introducing an external term to the system. Employing chaos theory, we showcase the chaotic tendencies of the perturbed dynamical system. Additionally, a sensitivity analysis using the Runge-Kutta method reveals the solution’s stability under slight variations in initial conditions. Innovatively, the paper utilizes the planar dynamical system technique to construct various solitons within the governing model. This research provides novel insights into the behavior of the (2+1)-dimensional cmKdV equation and its applications in applied magnetism and nanophysics.

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Funding

Princess Nourah bint Abdulrahman University Researchers Supporting Project number (PNURSP2024R 371), Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia.

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Authors and Affiliations

  1. School of Mathematical Sciences, Jiangsu University, Zhenjiang, 212013, Jiangsu, People’s Republic of China

    Mati ur Rahman & Mei Sun

  2. Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon

    Mati ur Rahman & Dumitru Baleanu

  3. University of Massachusetts Chan Medical School (UMASS), 55 Lake Avenue North, Worcester, MA, 01655, USA

    Yeliz Karaca

  4. Massachusetts Institute of Technology (MIT), 77 Massachusetts Avenue, Cambridge, MA, 02139, USA

    Yeliz Karaca

  5. Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh, 11671, Saudi Arabia

    Wafa F. Alfwzan

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  1. Mati ur Rahman
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  2. Yeliz Karaca
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  4. Dumitru Baleanu
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ur Rahman, M., Karaca, Y., Sun, M. et al. Complex behaviors and various soliton profiles of (2+1)-dimensional complex modified Korteweg-de-Vries Equation. Opt Quant Electron 56, 878 (2024). https://doi.org/10.1007/s11082-024-06514-4

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