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We study a 1-D array of Josephson coupled superconducting grains with kineticinductance which dominates over the Josephson inductance. In this limit thedynamics of excess Cooper pairs in the array is described in terms of chargesolitons, created by polarization of the grains. We analyze the dynamics ofthese topological excitations, which are dual to the fluxons in a longJosephson junction, using the continuum sine-Gordon model. We find that theirclassical relativistic motion leads to saturation branches in the I-Vcharacteristic of the array. We then discuss the semi-classical quantization ofthe charge soliton, and show that it is consistent with the large kineticinductance of the array. We study the dynamics of a quantum charge soliton in aring-shaped array biased by an external flux through its center. If thedephasing length of the quantum charge soliton is larger than the circumferenceof the array, quantum phenomena like persistent current and coherent currentoscillations are expected. As the characteristic width of the charge soliton isof the order of 100 microns, it is a macroscopic quantum object. We discuss thedephasing mechanisms which can suppress the quantum behaviour of the chargesoliton.Comment: 26 pages, LaTex, 7 Postscript figure

Charge solitons in one-dimensional arrays of serially coupled Josephson junctions