The Shocks in Josephson Transmission Line Revisited

Abstract

We continue our previous studies of the localized travelling waves, more specifically, of the shocks and the kinks, propagating in the series‐connected 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 study the similarities and the dissimilarities between the shocks and the kinks in the lossy JTL. We also find the particular cases, when the nonlinear equation, describing weak travelling wave in the lossy JTL can be integrated in terms of elementary functions.This article is protected by copyright. All rights reserved.

Exact Analytical Solutions for the Kinks, the Solitons and the Shocks in Discrete Nonlinear Transmission Line with Nonlinear Capacitance

“…The point V = V 2 can be the point of either stable, or unstable equilibrium. (We met with similar dichotomy while studying localized travelling waves in JTL [16] ). The waves corresponding to the stable equilibrium at the point V = V 2 we called the shocks, to the unstable equilibriumthe kinks.…”

“…(we assume for the sake of definiteness that β > 0 and V 1, V 2 > 0). The elementary solution of (54) satisfying the boundary conditions (19) is of the form [16]…”