  We investigate the charge transport in one-dimensional arrays of Josephson
junctions. In the interesting regime of "small charge solitons" (polarons), the
charge dynamics is strongly influenced by the polaronic effects, i.e., by
dressing of a Cooper pair by charge dipoles. In particular, the soliton's mass
in this regime scales approximately as inverse square of the Josephson energy.
We employ two theoretical techniques: the many body tight-binding approach and
the mean-field approach. Results of the two approaches agree in the regime of
"small charge solitons".
