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Non-Linear Plasma Wave Dynamics: Investigating Chaos in Dynamical Systems

Author

Listed:
  • Raymond Ghandour

    (College of Engineering and Technology, American University of the Middle East, Egaila 54200, Kuwait)

  • Abdullah S. Karar

    (College of Engineering and Technology, American University of the Middle East, Egaila 54200, Kuwait)

  • Zaher Al Barakeh

    (College of Engineering and Technology, American University of the Middle East, Egaila 54200, Kuwait)

  • Julien Moussa H. Barakat

    (College of Engineering and Technology, American University of the Middle East, Egaila 54200, Kuwait)

  • Zia Ur Rehman

    (Department of Mathematical Sciences, University of Engineering & Technology, Taxila 47050, Punjab, Pakistan)

Abstract

This work addresses the significant issue of plasma waves interacting with non-linear dynamical systems in both perturbed and unperturbed states, as modeled by the generalized Whitham–Broer–Kaup–Boussinesq–Kupershmidt (WBK-BK) Equations. We investigate analytical solutions and the subsequent emergence of chaos within these systems. Initially, we apply advanced mathematical techniques, including the transform method and the G ′ G 2 method. These methods allow us to derive new precise solutions and enhance our understanding of the non-linear processes dominating plasma wave dynamics. Through a systematic analysis, we identify the conditions under which the system transitions from orderly patterns to chaotic behavior. This investigation provides valuable insights into the fundamental mechanisms of non-linear wave propagation in plasmas. Our results highlight the dynamic interplay between non-linearity and variation, leading to chaos, which may be useful in predicting and potentially controlling similar phenomena in practical applications.

Suggested Citation

  • Raymond Ghandour & Abdullah S. Karar & Zaher Al Barakeh & Julien Moussa H. Barakat & Zia Ur Rehman, 2024. "Non-Linear Plasma Wave Dynamics: Investigating Chaos in Dynamical Systems," Mathematics, MDPI, vol. 12(18), pages 1-17, September.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:18:p:2958-:d:1484011
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    References listed on IDEAS

    as
    1. Ramamoorthy, Ramesh & Rajagopal, Karthikeyan & Leutcho, Gervais Dolvis & Krejcar, Ondrej & Namazi, Hamidreza & Hussain, Iqtadar, 2022. "Multistable dynamics and control of a new 4D memristive chaotic Sprott B system," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
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