Analysis of voltage and current flow of electrical transmission lines through mZK equation

• Main Authors: M. Ali Akbar, Md. Abdul Kayum, M.S. Osman, Abdel-Haleem Abdel-Aty, Hichem Eleuch
• Format: Article
• Language: English
• Published: Elsevier 2021-01-01
• Series: Results in Physics
• Subjects: Solitons; Nonlinear evolution equations; Sine-Gordon expansion method; Modified simple equation method; Modified Zakharov-Kuznetsov equation
• Online Access: http://www.sciencedirect.com/science/article/pii/S221137972032115X

Discrete networks, nonlinear networks, high speed computer data buses, computer network connections, and cable signal distribution are analyzed using the modified Zakharov-Kuznetsov (mZK) equation as a model governing the propagation in the electrical transmission lines. In this study, we establish viable extensive traveling wave solutions with the familiar singular kink type, kink type, bell-type solution, singular bell-type solution, t-type solution, and some advanced soliton solutions through the modified simple equation (MSE) and the sine-Gordon expansion methods. The established solutions are highly stable, resilient and capable to travel long distance. The solutions obtained can determine the voltage and current flow that can be used to design the transmission lines. The density plot and three-dimensional diagrams of the solutions obtained illustrate the voltage and current distributions in the transmission line. The traveling wave solutions are found in closed-form which simplify their utilization. The implemented methods are compatible for the extraction of traveling wave solutions.