The Shocks in Josephson Transmission Line Revisited

Abstract

We continue our previous studies of the shocks in the lossy Josephson transmission line (JTL). The article consists of two parts. In the first part, we analyze 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 oscillatory behavior with leading peaks resembling solitary waves if the losses are weak.