The kinks, the solitons and the shocks in series connected discrete Josephson transmission lines

Abstract

<div>We analytically study wave propagation in the discrete Josephson transmission lines (JTL), constructed from Josephson junctions (JJ) and capacitors. Our approach is based on the quasi-continuum approximation, which we discuss in details. The approximation allows to take into account the intrinsic dispersion in the discrete JTL. Due to competition between such dispersion and the nonlinearity, in the dissipationless JTL there exist running waves in the form of supersonic kinks and solitons. We also study the effect of dissipation in the system and find that in the presence of the resistors, shunting the JJ and/or in series with the ground capacitors, the only possible stationary running waves are the shock waves</div>