Discrete rotating wave solutions for system of globally coupled Josephson junctions

For a general system of Josephsons junctions, when the number of junctions is sufficiently large, there exist discrete rotating wave solutions as long as either the resistance of the load is not zero or the capacitance of the load is not infinity. Here, we show that these discrete rotating wave solutions, together with all their derivatives, converge to a certain wave form exponentially fast when the number of junctions in the array tends to infinity. Moreover, when the number of junctions is sufficiently large the discrete rotating wave solution is unique up to a time shift and permutation.