Traveling and localized solitary wave solutions of the nonlinear electrical transmission line model equation

Abstract

Analytical solutions describing the kink–antikink type, hyperbolic, trigonometric, doubly periodic, localized bright and dark soliton like, breather and rational periodic train solutions to the discrete nonlinear electrical transmission line in $$(2+1)$$ -dimensions have been investigated with the Kudryashov method, the fractional linear transform method, and the simplest equation method with its modified and extended versions. Consequently, many new and more general explicit forms of traveling waves are retrieved under parametric conditions. The 3D, 2D, and density profile of some of the obtained results are numerically simulated by selecting suitable values of the various parameters of the NLTL model equation. Furthermore, all the obtained results were checked and verified by putting back into the considered nonlinear transmission line model equation with Maple and Mathematica software. The acquired results show the validity and reliability of the proposed schemes to the studied nonlinear electrical transmission line model.