  We analyze a new long wave model describing the electrodynamics of an array
of point Josephson junctions in a superconducting cavity. It consists in a wave
equation with Dirac delta function sine nonlinearities. We introduce an adapted
spectral problem whose spectrum gives the resonances in the current-voltage
characteristic curve of any array. Using the associated inner product and
eigenmodes, we establish that at the resonances the solution is described by
two simple ordinary differential equations.
