[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.

In this paper, we are using a hybrid electrical line meaning it is constituted by nonlinear inductors and nonlinear capacitors to derive two new set of nonlinear partial differential equations which govern the dynamics of solitary waves in the obtained lines. We therefore construct solitary wave solutions of the two set of equations by using direct and effective mathematical methods like that of Bogning-Djeumen Tchaho-Kofane [16-21]. This has permitted to discover that it is simultaneously propagated in one of the hybrid lines a set of two solitary waves of type (Kink; Kink) and in the other hybrid electrical line a set of two solitary waves of type (Pulse; Pulse) when the conditions we have elaborated are respected.

Hybrid Electrical Line, Construction, Soliton Solution, Solitary Wave, Nonlinear Partial Differential Equation, Kink, Pulse

[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] A. M. Wazwaz, A reliable treatment of the physical structure for the nonlinear equation K(m,n), Appl. Math. Comput, 163, (2005) 1081-1095. [03] 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. [04] M. L. Wang, Exact solutions for a compound Käv- Burgers equation, Phys. Lett. A. 213, (1996) 279-287. [05] E. Fan, Extended tanh-function method and its applications to nonlinear equations, Phys. Lett. A, 277, (2000) 212-218. [06] E. Fan, J. Zhang, A note on the homogeneous balance method, Phys. Lett. A, 305, (2002) 383-392. [07] 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. [08] Z. Feng, The first integral method to study the Burgers – Korteweg-de-Vries equation, J. Phys. Lett. A. 35, (2002), 343-349. [09] Z. Feng, On explicit exat solutions for the Lienard equation and its applications, J. Phys. Lett. A. 293, (2002), 57-66. [10] Z. Feng, On explicit exact solutions to compound Burgers- KdV equation, J. Math. Anal. Appl. 328, (2007), 1435-1450. [11] 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). [12] 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). [13] 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). [14] 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. 85 (3), 1979–2016 (2016). [15] Seadawy, A. R., Lu, D.: Bright and dark solitary wave soliton solutions for the generalized higher ordernonlinear Schrodinger equation and its stability. Results Phys. 7, 43–48 (2017). [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.