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Analyzing the bifurcation, chaos and soliton solutions to (3+1)-dimensional nonlinear hyperbolic Schrödinger equation

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  • Nadeem, Muhammad
  • Hayat, Tasawar

Abstract

Water wave development, soliton dynamics and electromagnetic field propagation are just a few phenomena that are studied using the (3+1)-dimensional nonlinear hyperbolic Schrödinger model (NLHSM). This work extracts unique soliton solutions such as solitary, dark periodic, combination of dark and bright solutions, and rational wave solutions by analyzing the NLHSM using the modified Sardar sub-equation technique (MSSET). Also, the chaotic structure for the governing model is examined with and without disturbance using chaos theory and bifurcation theory. The innovations of our research are in discovering hitherto unexplored bifurcation situations and chaotic behaviors within the governing equation. The focus of these investigations is on the solutions of nonlinear dynamics, which are illustrated using density plots, 3-D plots, 2-D curves, and pertinent physical property descriptions. Outcomes demonstrate the value of NLHSM for generating soliton solutions and evaluating them in nonlinear models, offering useful numerical tools for applied mathematics.

Suggested Citation

  • Nadeem, Muhammad & Hayat, Tasawar, 2024. "Analyzing the bifurcation, chaos and soliton solutions to (3+1)-dimensional nonlinear hyperbolic Schrödinger equation," Chaos, Solitons & Fractals, Elsevier, vol. 185(C).
    • Handle: RePEc:eee:chsofr:v:185:y:2024:i:c:s0960077924007422
    DOI: 10.1016/j.chaos.2024.115190
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    1. Yusufoğlu, Elcin & Bekir, Ahmet, 2008. "Exact solutions of coupled nonlinear evolution equations," Chaos, Solitons & Fractals, Elsevier, vol. 37(3), pages 842-848.
    2. Muhammad Nadeem & Mouad M. H. Ali & Arzu Akbulut, 2023. "Analytical and Approximate Solutions of the Nonlinear Gas Dynamic Equation Using a Hybrid Approach," Journal of Mathematics, Hindawi, vol. 2023, pages 1-7, April.
    3. Tariq, Kalim U. & Bekir, Ahmet & Nisar, Sana, 2023. "The dynamical structures of the Sharma–Tasso–Olver model in doubly dispersive medium," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    4. Changjin Xu & Muhammad Farman & Zixin Liu & Yicheng Pang, 2024. "Numerical Approximation And Analysis Of Epidemic Model With Constant Proportional Caputo Operator," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 32(02), pages 1-17.
    5. Yokus, Asıf & Isah, Muhammad Abubakar, 2023. "Dynamical behaviors of different wave structures to the Korteweg–de Vries equation with the Hirota bilinear technique," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 622(C).
    6. Michael Vrugt & Tobias Frohoff-Hülsmann & Eyal Heifetz & Uwe Thiele & Raphael Wittkowski, 2023. "From a microscopic inertial active matter model to the Schrödinger equation," Nature Communications, Nature, vol. 14(1), pages 1-18, December.
    7. Qura Tul Ain & Muhammad Nadeem & Devendra Kumar & Mohd Asif Shah & S. E. Najafi, 2023. "Analysis of Fuzzy Differential Equation with Fractional Derivative in Caputo Sense," Advances in Mathematical Physics, Hindawi, vol. 2023, pages 1-8, April.
    8. Badshah, Fazal & Tariq, Kalim U. & Bekir, Ahmet & Tufail, R. Nadir & Ilyas, Hamza, 2024. "Lump, periodic, travelling, semi-analytical solutions and stability analysis for the Ito integro-differential equation arising in shallow water waves," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    9. Tomar, Saurabh & Singh, Mehakpreet & Vajravelu, Kuppalapalle & Ramos, Higinio, 2023. "Simplifying the variational iteration method: A new approach to obtain the Lagrange multiplier," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 640-644.
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