The shocks in Josephson transmission line revisited

TL;DR

This paper revisits shock phenomena in lossy Josephson transmission lines, analyzing wave scattering, shock and kink solutions, and revealing soliton-like features under weak loss conditions.

Contribution

It extends previous work by analyzing shock and kink behaviors in lossy JTLs, including scattering properties and soliton-like shock profiles.

Findings

Sound wave scattering coefficients calculated

Existence of kinks in lossy JTLs demonstrated

Shock profiles show soliton-like features with weak losses

Abstract

We continue our previous studies of the shocks in the lossy Josephson transmission line (JTL). The paper consists of two parts. In the first part we analyse the scattering of the "sound' (small amplitude small wave vector harmonic wave) on the shock wave and calculate the reflection and the transmission coefficients. In the second part we show that the kinks, which we previously studied only in the lossless JTL, exist also in the lossy JTL and study the similarities and the dissimilarities between the shocks and the kinks there. We find that the nonlinear equation describing the weak kinks and the weak shocks can be integrated (in particular cases) in terms of elementary functions. We also show that the profile of the shock in the lossy JTL demonstrates soliton-like features if the losses are weak.