New soliton solutions of the mZK equation and the Gerdjikov-Ivanov equation by employing the double G′/G,1/G-expansion method

Abstract

In the electrical transmission lines, the processing of cable signals distribution, computer networks, high-speed computer databases and discrete networks can be investigated by the modified Zakharov-Kuznetsov (mZK) equation as a data link propagation control model in the study of nonlinear Schrödinger type equations as well as in the analysis of the generalized stationary Gardner equation. The proposed Gerdjikov–Ivanov model can be used in the field of nonlinear optics, weakly nonlinear dispersion water waves, quantum field theory etc. In this work, we developed complete traveling wave solutions with specific t-type, kink type, bell-type, singular solutions, and periodic singular solutions to the proposed mZK equation and the Gerdjikov-Ivanov equation with the aid of the double G′/G,1/G- expansion method. These settled solutions are very reliable, durable, and authentic which can measure the fluid velocity and fluid density in the electrically conductive fluid and be able to analysis of the flow of current and voltage of long-distance electrical transmission lines too. These traveling wave solutions are available in a closed format and make them easy to use. The proposed method is consistent with the abstraction of traveling wave solutions.

Keywords

• The double (G′/G, 1/G)-expansion method
• The mZK equation
• The Gerdjikov-Ivanov equation
• Soliton solutions