[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’s Training College, University of Bamenda, Bamenda, Cameroon.

Nowadays, a soliton is considered as a future wave because it is a robust, a stable and a non-dissipative solitary wave. If one can use a soliton as a transmission signal in electrical lines, this will have advantages in the economic, technology and educative domains. Since the propagation of soliton is due to the interaction between nonlinearity and dispersion, it necessitates that the transmission medium should be nonlinear and dispersive. The physical system that one has chosen for this study is a Noguchi electrical line due to the fact that it is cheaper and very easy to manufacture than other transmission lines; then one find out analytically the variation that must undergo the charge of capacitors of that electrical line so that its transmission medium accepts the propagation of solitary wave of the wished type. The objective of this research is to define the analytical expression of the charge of capacitors in the line, to model higher-order nonlinear partial differential equations which govern the dynamics of those solitary waves in the line and to find out some exact solutions of solitary waves type of those equations. To attain our objective, one apply Kirchhoff laws to the circuit of a modified nonlinear Noguchi electrical line to model the higher-order nonlinear partial differential equations which describe the dynamics of those solitons. Then, one apply the direct and effective Bogning-Djeumen Tchaho-Kofane method based on the identification of basic hyperbolic function coefficients to construct some exact soliton solutions of modeled equations. The results obtained are supposed to permit: The amelioration of signals that will propagate in those line, the reduction of amplification stations of those lines, the facilitation of the choice of the type of the line relative to the type of signal one wishes to transmit, to augment the mathematical field knowledge, the manufacturing of new capacitors and new electrical lines susceptible of propagating those solitary waves.

Noguchi Electrical Line, Construction, Model, 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] 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). [03] 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). [04] 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). [05] 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). [06] A. M. Wazwaz, The tanh-coth method for new compactons and solitons solutions for the K(n,n) and K(n+1, n+1) equations, persive K(m,n) equations, Appl. Math. Comput, 188, (2007) 1930-1940. [07] M. L. Wang, Exact solutions for a compound Käv- Burgers equation, Phys. Lett. A. 213, (1996) 279-287. [08] E. Fan, Extended tanh-function method and its applications to nonlinear equations, Phys. Lett. A, 277, (2000) 212-218. [09] E. Fan, J. Zhang, A note on the homogeneous balance method, Phys. Lett. A, 305, (2002) 383-392. [10] 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. [11] A. M. Wazwaz, Solutions of compact and non compact structures for nonlinear Klein-Gordon type equation, Appl. Math. Comput, 134, (2003) 487-500. [12] A. M. Wazwaz, Traveling wave solutions of generalized forms of Burgers – KdV and Burgers Huxly equations, Appl. Math. Comput, 169, (2005) 639-656. [13] Z. Feng, The first integral method to study the Burgers – Korteweg-de-Vries equation, J. Phys. Lett. A. 35, (2002), 343-349. [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.