American Journal of Circuits, Systems and Signal Processing
Articles Information
American Journal of Circuits, Systems and Signal Processing, Vol.4, No.3, Sep. 2018, Pub. Date: Sep. 4, 2018
Construction of Solitary Wave Solutions of Higher-Order Nonlinear Partial Differential Equations Modeled in a Modified Nonlinear Noguchi Electrical Line
Pages: 36-44 Views: 39 Downloads: 46
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’s Training College, University of Bamenda, Bamenda, Cameroon.
Abstract
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.
Keywords
Noguchi Electrical Line, Construction, Model, Soliton Solution, Solitary Wave, Nonlinear Partial Differential Equation, Kink, Pulse
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