https://doi.org/10.1140/epjp/s13360-024-05194-z
Regular Article
Exploring dynamic behaviors of diverse electrical soliton pulses in lossy nonlinear electrical transmission lines: Insights from analytical method and linear stability analysis technique
1
Department of
Mathematics, Bangabandhu Sheikh Mujibur Rahman
Science and Technology University, 8100, Gopalganj, Bangladesh
2
Department of Electrical and
Electronic Engineering, Bangabandhu Sheikh
Mujibur Rahman Science and Technology University, 8100, Gopalganj, Bangladesh
3
Department of
Mathematics, University of Rajshahi, 6205, Rajshahi, Bangladesh
4
Department of
Mathematics, Rajshahi University of
Engineering and Technology, 6204, Rajshahi, Bangladesh
b
saifulslm6@gmail.com
c
pcgour2001@yahoo.com
Received:
9
September
2023
Accepted:
19
April
2024
Published online:
20
May
2024
The study aims to explore the intricate dynamics of various types of pulses within a nonlinear, lossy electrical transmission line, describing the propagation of electrical solitons in nonlinear dispersive media. In pursuit of these aims, an analytical method known as the unified method is employed to the nonlinear, lossy transmission lines periodically loaded with symmetric voltage-dependent capacitances. By applying Kirchhoff’s law in the continuum limit, a nonlinear partial differential equation for the voltage on the transmission line is derived. Subsequently, with the aid of the unified method, a variety of electrical soliton pulses, including dark, bright, singular, periodic singular, periodic W-shaped, and periodic waves, are obtained from the voltage equation. Additionally, stability analysis of the model is assessed using linear stability analysis technique, confirming the stability of dispersion. The coefficients of the nonlinear transmission lines model are found to play a substantial role in changing the shapes of the solitons. By adjusting the parameters for the obtained analytic solutions for nonlinear transmission lines to suitable values, the model can effectively modify the characteristics of the waves and produce desired wave profiles. The received solitons could find their applications in telecommunication systems to carry information and increase the bit rate of data. The ability of electrical soliton pulses to propagate with minimal dispersion makes them an efficient approach for transmitting data modulated as short pulses over long distances.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
