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Abstract

Herein, the series-connected Josephson transmission line (JTL), constructed from Josephson junctions, capacitors, and (possibly) resistors, is considered. It is shown that the compact travelling waves in the lossy JTL are the shocks, some of their properties including their velocity are studied. The velocity of shocks in the discrete lossy JTL is calculated. The continuum, the quasi-continuum, and the quasi-discrete approximations for the discrete JTL, both lossless and lossy, are thoroughly studied. In the framework of the latter, it is shown that the only compact travelling waves in the lossless JTL are the kinks and the solitons. On top of the continuum and the quasi-continuum approximations, the simple wave approximation, which decouples the JTL equations into two separate equations for the right- and left-going waves, is proposed. The approximation, in particular, allows to easily consider the formation of shocks in the lossy JTL.