  We consider the series-connected Josephson transmission line (JTL),
constructed from Josephson junctions, capacitors and (possibly) resistors. We
calculate the velocity of shocks in the discrete lossy JTL. We study thoroughly
the continuum and the quasi-continuum approximations to the discrete JTL, both
lossless and lossy. In the framework of these approximations we show that the
compact travelling waves in the lossless JTL are the kinks and the solitons,
and calculate their velocities. On top of each of the above mentioned
approximations, we propose the simple wave approximation, which decouples the
JTL equations into two separate equations for the right- and left-going waves.
The approximation, in particular, allows to easily consider the formation of
shocks in the lossy JTL.
