%0 Journal Article %T Lie group classification of the nonlinear transmission line model and exact traveling wave solutions %A Amtout, T. %A Er-Riani, M. %A El Jarroudi, M. %J Journal of Nonlinear Sciences and Applications %D 2022 %V 15 %N 4 %@ ISSN 2008-1901 %F Amtout2022 %X 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. %9 journal article %R 10.22436/jnsa.015.04.02 %U http://dx.doi.org/10.22436/jnsa.015.04.02 %P 267--275 %0 Journal Article %T Nonlinear Transmission Lines for Pulse Shaping in Silicon %A E. Afshari %A A. Hajimiri %J IEEE J. Solid-State Circuits %D 2005 %V 40 %F Afshari2005 %0 Journal Article %T Applications of Lie Symmetry Analysis to the Natural Convection Flow of Boundary Layer Past an Inclined Surface %A T. Amtout %A M. Er-Riani %A M. El Jarroudi %J Adv. Intell. Syst. Comput. %D 2022 %V 1418 %F Amtout2022 %0 Journal Article %T Lie Symmetry Analysis of a Class of Thermal Conduction Models %A H. Biyadi %A T. Amtout %A M. Er-Riani %A M. El Jarroudi %J Appl. Math. Sci. %D 2019 %V 13 %F Biyadi2019 %0 Book %T Symmetries and differential equations %A G. W. Bluman %A S. Kumei %D 1989 %I Springer-Verlag %C New York %F Bluman1989 %0 Journal Article %T Lie Symmetry Analysis and traveling wave solutions of equal width wave equation %A A. Chauhan %A R. Arora %A A. Tomar %J Proyecciones %D 2020 %V 39 %F Chauhan2020 %0 Journal Article %T Exact and soliton solutions to nonlinear transmission line model %A M. M. El-Borai %A H. M. El-Owaidy %A H. M. Ahmed %A A. H. Arnous %J Nonlinear Dyn. %D 2017 %V 87 %F El-Borai2017 %0 Journal Article %T Explicit Solution of General Fourth Order Time Fractional KdV Equation by Lie Symmetry Analysis %A H. Gandhi %A D. Singh %A A. Tomar %J AIP Conference Proceedings %D 2020 %V 2253 %F Gandhi2020 %0 Journal Article %T Conservation laws and exact series solution of fractional-order Hirota-Satsuma-coupled Korteveg-de Vries system by symmetry analysis %A H. Gandhi %A A. Tomar %A D. Singh %J Math. Methods Appl. Sci. %D 2021 %V 44 %F Gandhi2021 %0 Book %T CRC Handbook of Lie Group Analysis of Differential Equations %A N. Ibragimov %D 1995 %I CRC Press %C Boca Raton %F Ibragimov1995 %0 Journal Article %T Competent closed form soliton solutions to the nonlinear transmission and the low-pass electrical transmission lines %A M. A. Kayum %A M. Ali Akbar %A M. S. Osman %J Eur. Phys. J. Plus %D 2020 %V 135 %F Kayum2020 %0 Journal Article %T Multiple soliton solutions of the nonlinear partial differential equations describing the wave propagation in nonlinear low-pass electrical transmission lines %A D. Kumar %A A. R. Seadawy %A M. R. Haque %J Chaos Solitons Fractals %D 2018 %V 115 %F Kumar2018 %0 Journal Article %T Solitary wave solutions of nonlinear wave equation %A W. Malfliet %J Amer. J. Phys. %D 1992 %V 60 %F Malfliet1992 %0 Journal Article %T Analytical study for the ability of nonlinear transmission lines to generate solitons %A S. I. Mostafa %J Chaos Solitons Fractals %D 2009 %V 39 %F Mostafa2009 %0 Book %T Application of Lie Group to Differential Equation %A P. J. Olver %D 1986 %I Springer-Verlag %C New York %F Olver1986 %0 Book %T Group Analysis of Differential Equations %A L. V. Ovsiannikov %D 1982 %I Academic Press %C New York %F Ovsiannikov1982 %0 Journal Article %T A Simple Introduction to the Transmission-Line Modeling %A M. N. O. Sadiku %A L. C. Agba %J IEEE Trans. Circuits and Systems %D 1990 %V 37 %F Sadiku1990 %0 Journal Article %T The tanh-method for traveling wave solutions of nonlinear equations %A A.-M. Wazwaz %J Appl. Math. Comput. %D 2004 %V 154 %F Wazwaz2004 %0 Journal Article %T Analytic study of the fifth order integrable nonlinear evolution equations by using the tanh method %A A.-M. Wazwaz %J Appl. Math. Comput. %D 2006 %V 174 %F Wazwaz2006 %0 Journal Article %T The tanh method for travelling wave solutions to the Zhiber-Shabat equation and other related equations %A A.-M. Wazwaz %J Commun. Nonlinear Sci. Numer. Simul. %D 2008 %V 13 %F Wazwaz2008