Exact analytical solutions for the kinks, the solitons and the shocks in discrete nonlinear transmission line with nonlinear capacitance

TL;DR

This paper derives exact analytical solutions for various localized waves, including kinks, solitons, and shocks, in discrete nonlinear transmission lines with nonlinear capacitance, covering both lossless and lossy cases.

Contribution

It provides explicit formulas for the speeds and profiles of localized waves in nonlinear transmission lines, advancing understanding of wave behavior in such systems.

Findings

Exact solutions for lossless kink and soliton profiles and speeds.

Analytical expressions for dissipative kink and shock wave characteristics.

Comprehensive analysis of wave dynamics in nonlinear transmission lines.

Abstract

We studied discrete transmission lines constructed from ideal linear inductors and nonlinear capacitors (and possibly resistors). The localised travelling waves in the lossless transmission lines are the kinks and the solitons, which speeds and profiles were calculated. The localised travelling waves in the lossy transmission lines are the dissipative kinks and the shocks, which speeds and profiles were also calculated.