Resonances in spatially modulated long Josephson junctions

We have developed a theory for experimentally found resonances in one-dimen sional discrete Josephson transmission Lines. These resonances appear when both the inductive and capacitive interactions between junctions occur. The spectrum of linear electromagnetic waves propagating in this system contai ns many bands. We calculate the resonance voltages by making use of a mappi ng to the theory of Brillouin bands. The dependence of the resonance voltag es on the external magnetic field is found to be in good accord with experi ments on strip-line Josephson junction arrays and long Josephson junctions with periodically distributed microresistors. [S0163-1829(99)03241-5].