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Electrostatic Freak Waves in Pair-Ion and Pair-Ion-Electron Plasmas
Research Article | Published: 29 October 2025
ICCK Journal of Applied Mathematics Volume 1, Issue 3, 2025: 120-128
Volume 1, Issue 3, ICCK Journal of Applied Mathematics
Volume 1, Issue 3, 2025
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ICCK Journal of Applied Mathematics, Volume 1, Issue 3, 2025: 120-128

Open Access | Research Article | 29 October 2025
Electrostatic Freak Waves in Pair-Ion and Pair-Ion-Electron Plasmas
by
Muhammad Yaqoob Khan Muhammad Yaqoob Khan 1
Muhammad Waqar Ahmed Muhammad Waqar Ahmed 2 *
1 Department of Mathematics, Riphah International University, Islamabad, Pakistan
2 Department of Physics, Riphah International University, Islamabad, Pakistan
* Corresponding Author: Muhammad Waqar Ahmed, [email protected]
DOI: 10.62762/JAM.2025.698605
Received: 13 August 2025, Accepted: 29 September 2025, Published: 29 October 2025  
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Abstract
This work investigates the formation and dynamics of electrostatic freak waves in pair-ion (PI) and pair-ion--electron (PIE) plasmas. The analysis begins with the derivation of the Korteweg--de Vries (KdV) equations for both plasma configurations, from which the corresponding nonlinear and dispersive coefficients are obtained. By employing the wave superposition principle, the KdV equations are systematically reduced to the nonlinear Schrödinger equation (NLSE), enabling the exploration of modulation instability and rogue wave generation. Analytical solutions of the NLSE are utilized to construct parametric plots that elucidate the evolution of freak waves in PI and PIE plasmas. Comparative analysis reveals pronounced differences in the amplitude, localization, and structural properties of the freak waves in the two plasma environments, highlighting the critical role of electron contributions in shaping nonlinear wave phenomena.
Graphical Abstract
Electrostatic Freak Waves in Pair-Ion and Pair-Ion-Electron Plasmas
Keywords
wave phenomena
freak waves
Pair-Ion plasmas
Pair-Ion--Electron plasmas
NLS equation
reductive perturbation method
Data Availability Statement
Data will be made available on request.
Funding
This work was supported without any funding.
Conflicts of Interest
The authors declare no conflicts of interest.
Ethical Approval and Consent to Participate
Not applicable.
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Cite This Article
APA Style
Khan, M. Y., & Ahmed, M. W. (2025). Electrostatic Freak Waves in Pair-Ion and Pair-Ion-Electron Plasmas. ICCK Journal of Applied Mathematics, 1(3), 120–128. https://doi.org/10.62762/JAM.2025.698605
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CC BY Copyright © 2025 by the Author(s). Published by Institute of Central Computation and Knowledge. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
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