Limit and uniqueness of discrete rotating waves in large arrays of Josephson junctions

We study the limiting behaviour of discrete rotating wave solutions (also known as ponies on a merry-go-round or splay phase solutions) for large arrays of Josephson junctions. In particular, we prove that these solutions, together with all their derivatives, converge to a certain waveform 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.