Coupled soliton solutions of modeled equations in a Noguchi electrical line with crosslink capacitor

Abstract

An electrical line is one of the transmission media used worldwide for the transmission of signals. This is for the fact that it is less expensive and easy to manufacture than the other transmission media. In linear domain, the electrical lines transmit sinusoidal signals whose amplitude decreases exponentially and loss a lot of energy. It is therefore necessary to valorize electrical lines by enabling them to transmit solitary waves which are more stable and do not dissipate energy. This will be possible if the media of transmission line are dispersive and nonlinear. We define the analytical expressions that the charges of capacitors must obey so that the Noguchi electrical line with crosslink capacitor accepts to propagate a coupled solitary wave of the need type. The application of those definitions and Kirchhoff laws to the networks of a modified Noguchi electrical line with crosslink capacitor have enable to obtain new set of higher-order nonlinear partial differential equations which govern the dynamics of a coupled solitary wave in the said line. The construction of coupled solitary waves solutions of those set of equations by direct and effective mathematical methods notably that of Bogning-Djeumen Tchaho-Kofane [16–22] has permitted to discover that, solitary waves of type (Kink; Kink) and type (Pulse; Pulse) are easily propagated in that line when certain conditions we have elaborated are respected. The Noguchi electrical line with crosslink capacitor that we have studied is advantageous for the fact that it permits simultaneously the propagation of a set of two solitary waves contrary to a non-coupled Noguchi electrical line which only enables the propagation of one solitary wave when the signal considered is the voltage; the more we will multiply the crosslink in the line, the more we will multiply the simultaneous propagation of solitary wave in the line.