LIMIT AND UNIQUENESS OF DISCRETE ROTATING WAVES IN LARGE ARRAYS OF JOSEPHSON-JUNCTIONS

We study the limiting behaviour of discrete rotating wave solutions (a lso known as ponies on a merry-go-round or splay phase solutions) for large arrays of Josephson junctions. In particular, we prove that thes e solutions, together with all their derivatives, converge to a certai n waveform exponentially fast when the number of junctions in the arra y tends to infinity. Moreover, when the number of junctions is suffici ently large the discrete rotating wave solution is unique up to a time shift.