Geodesic
Lie group classification of the nonlinear transmission line model and exact traveling wave solutions
Amtout, T.1 ; Er-Riani, M.1 ; El Jarroudi, M.1
1 Department of Mathematics, Laboratory of Mathematics and Applications (LMA), Faculty of Sciences and Techniques, University Abdel Malek Essaadi, UAE, BP 416, Km 10, Ziaten, 90000, Tangier, Morocco
Journal of nonlinear sciences and its applications, Tome 15 (2022) no. 4, p. 267-275.

Voir la notice de l'article provenant de la source International Scientific Research Publications

A nonlinear transmission line (NLTL) model is very essential tools in understanding of propagation of electrical solitons which can propagate in the form of voltage waves in nonlinear dispersive media. These models are often formulated using nonlinear partial differential equations. One of the basic tools available to study these equations are numerical methods such as finite difference method, finite element method, etc, have been developed for nonlinear partial differential equations. These methods require a great amount of time and memory due to the discretization and usually the effect of round-off error causes loss of accuracy in the results. So in this paper, we use one of the most famous analytical methods the Lie group analysis due to Sophus Lie. One of the advantages of this approach is that requires only algebraic calculations. The main aim of this study is to explore the nonlinear transmission line model with arbitrary capacitor's voltage dependence, through the use of Lie group classification, we show that the specifying form of arbitrary capacitor's voltage are power law nonlinearity, exponential law nonlinearity and constant capacitance. The exact solutions and similarity reductions generated from the symmetries are also provided. Furthermore, translational symmetries were utilized to find a family of traveling wave solutions via the $\tanh$-method of the governing nonlinear problem.
DOI : 10.22436/jnsa.015.04.02
Classification : 76M60, 35C07, 35C08
Keywords: Lie group classification, non-linear line transmission, traveling wave solutions

Amtout, T. 1 ; Er-Riani, M. 1 ; El Jarroudi, M. 1

1 Department of Mathematics, Laboratory of Mathematics and Applications (LMA), Faculty of Sciences and Techniques, University Abdel Malek Essaadi, UAE, BP 416, Km 10, Ziaten, 90000, Tangier, Morocco 
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Amtout, T.; Er-Riani, M.; El Jarroudi, M. Lie group classification of the nonlinear transmission line model and exact traveling wave solutions. Journal of nonlinear sciences and its applications, Tome 15 (2022) no. 4, p. 267-275. doi : 10.22436/jnsa.015.04.02. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.015.04.02/

[1] Afshari, E.; Hajimiri, A. Nonlinear Transmission Lines for Pulse Shaping in Silicon, IEEE J. Solid-State Circuits, Volume 40 (2005), pp. 744-752

[2] Amtout, T.; Er-Riani, M.; Jarroudi, M. El Applications of Lie Symmetry Analysis to the Natural Convection Flow of Boundary Layer Past an Inclined Surface, Adv. Intell. Syst. Comput., Volume 1418 (2022), pp. 1053-1066

[3] Biyadi, H.; Amtout, T.; Er-Riani, M.; Jarroudi, M. El Lie Symmetry Analysis of a Class of Thermal Conduction Models, Appl. Math. Sci., Volume 13 (2019), pp. 1061-1067

[4] Bluman, G. W.; Kumei, S. Symmetries and differential equations, Springer-Verlag, New York, 1989

[5] Chauhan, A.; Arora, R.; Tomar, A. Lie Symmetry Analysis and traveling wave solutions of equal width wave equation, Proyecciones, Volume 39 (2020), pp. 179-198

[6] El-Borai, M. M.; El-Owaidy, H. M.; Ahmed, H. M.; Arnous, A. H. Exact and soliton solutions to nonlinear transmission line model, Nonlinear Dyn., Volume 87 (2017), pp. 767-773

[7] Gandhi, H.; Singh, D.; Tomar, A. Explicit Solution of General Fourth Order Time Fractional KdV Equation by Lie Symmetry Analysis, AIP Conference Proceedings, Volume 2253 (2020), pp. 1-14

[8] Gandhi, H.; Tomar, A.; Singh, D. Conservation laws and exact series solution of fractional-order Hirota-Satsuma-coupled Korteveg-de Vries system by symmetry analysis, Math. Methods Appl. Sci., Volume 44 (2021), pp. 14356-14370

[9] Ibragimov, N. CRC Handbook of Lie Group Analysis of Differential Equations, CRC Press, Boca Raton, 1995

[10] Kayum, M. A.; Akbar, M. Ali; Osman, M. S. Competent closed form soliton solutions to the nonlinear transmission and the low-pass electrical transmission lines, Eur. Phys. J. Plus, Volume 135 (2020), pp. 1-20 | DOI

[11] Kumar, D.; Seadawy, A. R.; Haque, M. R. Multiple soliton solutions of the nonlinear partial differential equations describing the wave propagation in nonlinear low-pass electrical transmission lines, Chaos Solitons Fractals, Volume 115 (2018), pp. 62-76

[12] Malfliet, W. Solitary wave solutions of nonlinear wave equation, Amer. J. Phys., Volume 60 (1992), pp. 650-654

[13] Mostafa, S. I. Analytical study for the ability of nonlinear transmission lines to generate solitons, Chaos Solitons Fractals, Volume 39 (2009), pp. 2125-2132

[14] Olver, P. J. Application of Lie Group to Differential Equation, Springer-Verlag, New York, 1986

[15] Ovsiannikov, L. V. Group Analysis of Differential Equations, Academic Press, New York, 1982

[16] Sadiku, M. N. O.; Agba, L. C. A Simple Introduction to the Transmission-Line Modeling, IEEE Trans. Circuits and Systems, Volume 37 (1990), pp. 991-999

[17] Wazwaz, A.-M. The tanh-method for traveling wave solutions of nonlinear equations, Appl. Math. Comput., Volume 154 (2004), pp. 713-723

[18] Wazwaz, A.-M. Analytic study of the fifth order integrable nonlinear evolution equations by using the tanh method, Appl. Math. Comput., Volume 174 (2006), pp. 289-299

[19] Wazwaz, A.-M. The tanh method for travelling wave solutions to the Zhiber-Shabat equation and other related equations, Commun. Nonlinear Sci. Numer. Simul., Volume 13 (2008), pp. 584-592

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