Modeling of Soliton Behavior in Nonlinear Transmission Line Systems

Sadia Medhit, Beenish, Fehaid Salem Alshammari () and Isha Bukhar
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Sadia Medhit: Department of Mathematics, PMAS-Arid Agriculture University, Rawalpindi 46300, Pakistan
Beenish: Department of Mathematics, Quaid-I-Azam University, Islamabad 45320, Pakistan
Fehaid Salem Alshammari: Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11564, Saudi Arabia
Isha Bukhar: Department of Mathematics, PMAS-Arid Agriculture University, Rawalpindi 46300, Pakistan

Mathematics, 2025, vol. 13, issue 18, 1-19

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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