Physics Journal
Articles Information
Physics Journal, Vol.4, No.3, Sep. 2018, Pub. Date: Oct. 9, 2018
Solitary Wave Solutions of Modified Telegraphist Equations Modeled in an Electrical Line
Pages: 29-36 Views: 252 Downloads: 160
Authors
[01] Tiague Takongmo Guy, Departement of Physics, Faculty of Science, University of Yaoundé 1, Yaoundé, Cameroon.
[02] Jean Roger Bogning, Departement of Physics, Higher Teacher Training College, University of Bamenda, Bamenda, Cameroon.
Abstract
In this paper, we are using an ordinary electrical line to find the modified Telegraphist equations in terms of current and voltage. Then, we define the nonlinear analytical shape that must respect the conductance per unit length so that the new obtained lines accept the propagation of solitary waves. From the analytical definition of the conductance of the modified Telegraphist equations, we obtain new nonlinear partial differential equations that govern the dynamics of solitary waves in the new lines. Having constructed the exact solitary wave solutions of the new higher-order nonlinear partial differential equations, we have confirmed that these lines accept the simultaneous propagation of a set of two signals which are current and voltage of type (Kink; Kink) or type (Pulse; Pulse). The obtained results have advantages generally in the domain of physics and particularly in the domain of engineering of telecommunication because the new lines obtained accept the propagation of solitary waves of type (Kink; Kink) or type (Pulse; Pulse) on longer distances maintaining their shape, their velocity, without loss of energy contrary to sinusoidal waves that we have obtained with non-modified Telegraphist equations whose amplitude decreases exponentially and loss a lot of energy.
Keywords
Telegraphist Equations, Construction, Model, Soliton Solution, Solitary Wave, Nonlinear Partial Differential Equation, Kink, Pulse
References
[01] J. R. Bogning, A. S. Tchakoutio Nguetcho, T. C. Kofané, Gap solitons coexisting with bright soliton in nonlinear fiber arrays. International Journal of nonlinear science and numerical simulation, Vol. 6 (4), (2005) 371-385.
[02] Dianchen, L., Seadawy, A., Arshad, M.: Applications of extended simple equation method on unstable nonlinear Schrodinger equations. Opt. Int. J. Light Electron Opt. 140, 136–144 (2017).
[03] Ekici, M., Zhou, Q., Sonmezoglu, A., Moshokoa, S. P., Zaka Ullah, M., Biswas, A., Belic, M.: Solitons in magneto-optic waveguides by extended trial function scheme. Superlattices Microstruct. 107, 197–218 (2017c).
[04] Jawad, A. J. M., Mirzazadeh, M., Zhou, Q., Biswas, A.: Optical solitons with anti-cubic nonlinearity using three integration schemes. Superlattices Microstruct. 105, 1–10 (2017).
[05] Mirzazadeh, M., Ekici, M., Sonmezoglu, A., Eslami, M., Zhou, Q., Kara, A. H., Milovic, D., Majid, F. B., Biswas, A., Belic, M.: Optical solitons with complex Ginzburg–Landau equation. Nonlinear Dyn. 8 5 (3), 1979–2016 (2016).
[06] Seadawy, A. R., Lu, D.: Bright and dark solitary wave soliton solutions for the generalized higher order nonlinear Schrodinger equation and its stability. Results Phys. 7, 43–48 (2017).
[07] A. M. Wazwaz, A reliable treatment of the physical structure for the nonlinear equation K(m,n), Appl. Math. Comput, 163, (2005) 1081-1095.
[08] A. M. Wazwaz, Explicit traveling waves solutions of variants of the K(n,n) and ZK(n,n) equations with compact and non compact structures, Appl. Math. Comput, 173, (2006) 213-220.
[09] M. L. Wang, Exact solutions for a compound Käv- Burgers equation, Phys. Lett. A. 213, (1996) 279-287.
[10] E. Fan, Extended tanh-function method and its applications to nonlinear equations, Phys. Lett. A, 277, (2000) 212-218.
[11] E. Fan, J. Zhang, A note on the homogeneous balance method, Phys. Lett. A, 305, (2002) 383-392.
[12] Y. B. Zhou, M. L. Wang, Y. M. Wang, Periodic wave solutions to a coupled KdV equations with variable coefficients, Phys. Lett. A, 308, (2003) 31-37.
[13] A. M. Wazwaz, Solutions of compact and non compact structures for nonlinear Klein-Gordon type equation, Appl. Math. Comput, 134, (2003) 487-500.
[14] Z. Feng, On explicit exat solutions for the Lienard equation and its applications, J. Phys. Lett. A. 293, (2002), 57-66.
[15] Z. Feng, On explicit exact solutions to compound Burgers- KdV equation, J. Math. Anal. Appl. 328, (2007), 1435-1450.
[16] J. R. Bogning, C. T. Djeumen Tchaho and T. C. Kofané, “Construction of the soliton solutions of the Ginzburg-Landau equations by the new Bogning-Djeumen Tchaho-Kofané method”, Phys. Scr, Vol. 85, (2012), 025013-025017.
[17] J. R. Bogning, C. T. Djeumen Tchaho and T. C. Kofané, “Generalization of the Bogning- Djeumen Tchaho-Kofane Method for the construction of the solitary waves and the survey of the instabilities”, Far East J. Dyn. Sys, Vol. 20, No. 2, (2012), 101-119.
[18] C. T. Djeumen Tchaho, J. R. Bogning, and T. C. Kofané, “Modulated Soliton Solution of the Modified Kuramoto-Sivashinsky's Equation”, American Journal of Computational and Applied Mathematics”, Vol. 2, No. 5, (2012), 218-224.
[19] C. T. Djeumen Tchaho, J. R. Bogning and T. C. Kofane, “Multi-Soliton solutions of the modified Kuramoto-Sivashinsky’s equation by the BDK method”, Far East J. Dyn. Sys. Vol. 15, No. 2, (2011), 83-98.
[20] C. T. Djeumen Tchaho, J. R. Bogning and T. C. Kofane, “Construction of the analytical solitary wave solutions of modified Kuramoto-Sivashinsky equation by the method of identification of coefficients of the hyperbolic functions”, Far East J. Dyn. Sys. Vol. 14, No. 1, (2010), 14-17.
[21] J. R. Bogning, “Pulse Soliton Solutions of the Modified KdV and Born-Infeld Equations” International Journal of Modern Nonlinear Theory and Application, 2, (2013), 135-140.
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