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

Raymond Ghandour (), Abdullah S. Karar (), Zaher Al Barakeh, Julien Moussa H. Barakat () and Zia Ur Rehman
Additional contact information
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

Mathematics, 2024, vol. 12, issue 18, 1-16

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.

Keywords: soliton solutions; bifurcation; Whitham–Broer–Kaup–Boussinesq–Kupershmidt; plasma wave; chaotic behavior (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/18/2958/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/18/2958/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:12:y:2024:i:18:p:2958-:d:1484011

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().