Analytical studies on waves in nonlinear transmission line media

Zehra Pinar

Abstract


In this study, we introduce the lossy nonlinear transmission line equation, which is the dissipative-dispersive equation and an important problem of electrical transmission lines. For the engineers and physicist, the equation and its exact solutions are important so to obtain the exact solutions; one of the modifications of auxiliary equation method based on Chebyshev differential equation is studied. The results are discussed and given in details. Recently, the studies of lossy transmission line equation have been challenging, thus, it is believed that the proposed solutions will be key part of further studies for waves in nonlinear transmission line media, which has mixed dissipative-dispersive behavior.


Keywords


Chebyshev equation; Auxiliary equation method; Lossy transmission line equation, Travelling wave solutions

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References


Tchier, F., Yusuf, A., Aliyu, A. I. & Inc, M. (2017). Soliton solutions and conservation laws for lossy nonlineartransmission line equation. Superlattices and Microstructures, 107, 320-336.

Kengne, E. & Vaillancourt, R. (2007). Propagation of solitary waves on lossy nonlinear transmission lines. International Journal of Modern Physics B, 23, 1-18.

Koon, K.T.V., Leon, J., Marquie, P. & Tchofo-Dinda, P. (2007). Cutoff solitons and bistability of the discrete inductance- capacitance electrical line: theory and experiments. Physical review. E, 75, 1-8.

Afshari, E. & Hajimiri, A. (2005). Nonlinear transmission lines for pulse shaping in silicon. IEEE Journal of Solid-State Circuits, 40, (3) : 744-752.

Sataric, M.V., Bednar, N., Sataric, B.M. & Stojanovic, G.A. (2009). Filaments as nonlinear RLC transmission lines. International Journal of Modern Physics B, 23(22), 4697-4711.

Mostafa, S.I. (2009). Analytical study for the ability of nonlinear transmission lines to generate solitons. Chaos, Solitons & Fractals, 39(5), 2125-2132.

Rosenau, P. (1986). A Quasi-Continuous Description of a Nonlinear Transmission Line. Physica Scripta, 34, 827-829.

Yomba, E. (2006). The modified extended Fan sub-equation method and its application to the (2+1)-dimensional Broer-Kaup-Kupershmidt equation. Chaos, Solitons & Fractals, 27, 187-196.

Sirendaoreji. (2007). Auxiliary equation method and new solutions of Klein–Gordon equations. Chaos, Solitons and Fractals, 31, 943–950.

Yomba, E. (2007). A generalized auxiliary equation method and its application to nonlinear Klein–Gordon and generalized nonlinear Camassa–Holm equations. Physics Letters A, 372, 1048–1060.

Yong, C., Biao, L. & Hong-Quing Z. (2003). Generalized Riccati equation expansion method and its application to Bogoyaylenskii’s generalized breaking soliton equation. Chinese Physics, 12, 940–946.

Pinar, Z., Öziş, T. (2013). An Observation on the Periodic Solutions to Nonlinear Physical models by means of the auxiliary equation with a sixth-degree nonlinear term. Communications in Nonlinear Science and Numerical Simulation, 18, 2177-2187.

Pinar, Z. & Öziş, T. (2015). A remark on a variable-coefficient Bernoulli equation based on auxiliary equation method for nonlinear physical systems. arXiv:1511.02154v1

Wazwaz, A. M. (2009). Partial Differential Equations and Solitary Wave Theory. Higher Education Press - Springer-Verlag, Beijing and Berlin.

Wazwaz, A. M. (2002). Partial Differential Equations: Methods and Applications. Balkema, Leiden.

Wazwaz, A. M. (2008). The tanh method for travelling wave solutions to the Zhiber–Shabat equation and other related equations. Communications in Nonlinear Science and Numerical Simulation, 13, 584–592.

Wazwaz, A. M. (2007). The Tanh-Coth Method Combined with the Riccati Equation for Solving the KDV Equation. Arab Journal of Mathematics and Mathematical Sciences, 1, 27–34.

Yong, X., Zeng, X., Zhang, Z. & Chen, Y. (2009). Symbolic computation of Jacobi elliptic function solutions to nonlinear differential-difference equations. Computers & Mathematics with Applications, 57, 1107-1114.

Zhang, H. (2009). A Note on Some Sub-Equation Methods and New Types of Exact Travelling Wave Solutions for Two Nonlinear Partial Differential Equations. Acta Applicandae Mathematicae, 106, 241-249.

Pinar, Z. & Öziş, T. (2015). Observations on the class of ‘‘Balancing Principle’’ for nonlinear PDEs that can be treated by the auxiliary equation method. Nonlinear Analysis: Real World Applications, 23, 9–16.

Rivlin, Theodore J. (1974). The Chebyshev polynomials. Pure and Applied Mathematics. Wiley-Interscience [John Wiley & Sons], New York-London-Sydney.

Krall, A. M. (2002). Hilbert Space, Boundary Value Problems and Orthogonal Polynomials. Birkhäuser Verlag, Basel-Boston – Berlin

Pinar, Z. & Kocak, H. (2018). Exact solutions for the third-order dispersive-Fisher equations. Nonlinear Dynamics, 91(1), 421-426.

Kocak, H. & Pinar, Z. (2018). On solutions of the fifth-order dispersive equations with porous medium type non-linearity. Waves in Random and Complex Media, 28(3), 516-522.




DOI: http://dx.doi.org/10.11121/ijocta.01.2019.00597

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