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Mathematics
Volume 13
Issue 18
10.3390/math13182997
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

Modeling of Soliton Behavior in Nonlinear Transmission Line Systems

by
Sadia Medhit
1,
Beenish
2,
Fehaid Salem Alshammari
3,* and
Isha Bukhar
1
1
Department of Mathematics, PMAS-Arid Agriculture University, Rawalpindi 46300, Pakistan
2
Department of Mathematics, Quaid-I-Azam University, Islamabad 45320, Pakistan
3
Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11564, Saudi Arabia
*
Author to whom correspondence should be addressed.
Mathematics 2025, 13(18), 2997; https://doi.org/10.3390/math13182997
Submission received: 3 August 2025 / Revised: 11 September 2025 / Accepted: 15 September 2025 / Published: 16 September 2025
(This article belongs to the Special Issue Mathematical Modelling, Analysis, and Optimization for Engineering and Mechanics)
Versions Notes

Abstract

This study focuses on the nonlinear partial differential equation known as the Lonngren wave equation, which plays a significant role in plasma physics, nonlinear wave propagation, and astrophysical research. By applying a suitable wave transformation, the nonlinear model is reduced to an ordinary differential equation. Analytical wave solutions of the Lonngren wave equation are then derived using the extended direct algebraic method. The physical behavior of these solutions is illustrated through 2D, 3D, and contour plots generated in Mathematica. Finally, the stability analysis of the Lonngren wave equation is discussed.
Keywords: Lonngren wave equation; extended direct algebraic method; spiral group Lonngren wave equation; extended direct algebraic method; spiral group

Share and Cite

MDPI and ACS Style

Medhit, S.; Beenish; Alshammari, F.S.; Bukhar, I. Modeling of Soliton Behavior in Nonlinear Transmission Line Systems. Mathematics 2025, 13, 2997. https://doi.org/10.3390/math13182997

AMA Style

Medhit S, Beenish, Alshammari FS, Bukhar I. Modeling of Soliton Behavior in Nonlinear Transmission Line Systems. Mathematics. 2025; 13(18):2997. https://doi.org/10.3390/math13182997

Chicago/Turabian Style

Medhit, Sadia, Beenish, Fehaid Salem Alshammari, and Isha Bukhar. 2025. "Modeling of Soliton Behavior in Nonlinear Transmission Line Systems" Mathematics 13, no. 18: 2997. https://doi.org/10.3390/math13182997

APA Style

Medhit, S., Beenish, Alshammari, F. S., & Bukhar, I. (2025). Modeling of Soliton Behavior in Nonlinear Transmission Line Systems. Mathematics, 13(18), 2997. https://doi.org/10.3390/math13182997

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