Research Article
Open Access
Electrostatic Freak Waves in Pair-Ion and Pair-Ion-Electron Plasmas
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]
Volume 1, Issue 3
2025
Received: 13 August 2025
Accepted: 29 September 2025
Published: 29 October 2025
Article Information
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
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.
References
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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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TY - JOUR AU - Khan, Muhammad Yaqoob AU - Ahmed, Muhammad Waqar PY - 2025 DA - 2025/10/29 TI - Electrostatic Freak Waves in Pair-Ion and Pair-Ion-Electron Plasmas JO - ICCK Journal of Applied Mathematics T2 - ICCK Journal of Applied Mathematics JF - ICCK Journal of Applied Mathematics VL - 1 IS - 3 SP - 120 EP - 128 DO - 10.62762/JAM.2025.698605 UR - https://www.icck.org/article/abs/JAM.2025.698605 KW - wave phenomena KW - freak waves KW - Pair-Ion plasmas KW - Pair-Ion--Electron plasmas KW - NLS equation KW - reductive perturbation method AB - 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. SN - 3068-5656 PB - Institute of Central Computation and Knowledge LA - English ER -
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@article{Khan2025Electrosta,
author = {Muhammad Yaqoob Khan and Muhammad Waqar Ahmed},
title = {Electrostatic Freak Waves in Pair-Ion and Pair-Ion-Electron Plasmas},
journal = {ICCK Journal of Applied Mathematics},
year = {2025},
volume = {1},
number = {3},
pages = {120-128},
doi = {10.62762/JAM.2025.698605},
url = {https://www.icck.org/article/abs/JAM.2025.698605},
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.},
keywords = {wave phenomena, freak waves, Pair-Ion plasmas, Pair-Ion--Electron plasmas, NLS equation, reductive perturbation method},
issn = {3068-5656},
publisher = {Institute of Central Computation and Knowledge}
}
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