Lie symmetry analysis, and traveling wave patterns arising the model of transmission lines

Adil Jhangeer; Ali R Ansari; Mudassar Imran; Beenish; Muhammad Bilal Riaz; Adil Jhangeer; Ali R Ansari; Mudassar Imran; Beenish; Muhammad Bilal Riaz

doi:10.3934/math.2024878

AIMS Mathematics

2024, Volume 9, Issue 7: 18013-18033. doi: 10.3934/math.2024878

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Research article

Lie symmetry analysis, and traveling wave patterns arising the model of transmission lines

1.
IT4Innovations, VSB–Technical University of Ostrava, Ostrava-Poruba, Czech Republic; muhammad.bilal.riaz@vsb.cz
2.
Department of Mathematics, Namal University, 30KM Talagang Road, Mianwali 42250, Pakistan
3.
Centre for Applied Mathematics and Bioinformatics (CAMB), Gulf University for Science and Technology, Kuwait; ansari.a@gust.edu.kw
4.
College of Humanities and Sciences, Ajman University, Ajman, UAE; mudassar.Imran@ajman.ac.ae
5.
Department of Mathematics, Quaid-I-Azam University 45320, Islamabad, Pakistan; beenishmasood2141@gmail.com
6.
Department of Computer Science and Mathematics, Lebanese American University, Byblos, Lebanon

Received: 20 March 2024 Revised: 01 May 2024 Accepted: 09 May 2024 Published: 27 May 2024
MSC : 22E60, 35C07, 35Q60

This work studies the behavior of electrical signals in resonant tunneling diodes through the application of the Lonngren wave equation. Utilizing the method of Lie symmetries, we have identified optimal systems and found symmetry reductions; we have also found soliton wave solutions by applying the tanh technique. The bifurcation and Galilean transformation are found to determine the model implications and convert the system into a planar dynamical system. In this experiment, the equilibrium state, sensitivity, and chaos are investigated and numerical simulations are conducted to show how the frequency and amplitude of alterations affect the system. Furthermore, local conservation rules are demonstrated in more detail to unveil the whole system of movements.
- Lonngren wave equation,
- bifurcation analysis,
- sensitivity analysis,
- Lyapunov exponent,
- multistability analysis,
- Lie point symmetry
Citation: Adil Jhangeer, Ali R Ansari, Mudassar Imran, Beenish, Muhammad Bilal Riaz. Lie symmetry analysis, and traveling wave patterns arising the model of transmission lines[J]. AIMS Mathematics, 2024, 9(7): 18013-18033. doi: 10.3934/math.2024878

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Abstract

This work studies the behavior of electrical signals in resonant tunneling diodes through the application of the Lonngren wave equation. Utilizing the method of Lie symmetries, we have identified optimal systems and found symmetry reductions; we have also found soliton wave solutions by applying the tanh technique. The bifurcation and Galilean transformation are found to determine the model implications and convert the system into a planar dynamical system. In this experiment, the equilibrium state, sensitivity, and chaos are investigated and numerical simulations are conducted to show how the frequency and amplitude of alterations affect the system. Furthermore, local conservation rules are demonstrated in more detail to unveil the whole system of movements.

References

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