Modulation instability of electromagnetic excitations in the nonlocal Josephson electrodynamics of thin magnetic superconducting films

The modulation instability of plane finite-amplitude nonlinear waves with the Josephson frequency is studied for a Josephson contact in thin nonmagnetic and magnetic (two-dimensional) superconducting films. Dispersion relations for the increments of small-amplitude perturbations are derived. Modulation instability is shown to develop in the finite range 0<Q<Q _b of the wavevectors of amplitude perturbations for the nonmagnetic films and for any perturbation wavevector 0<Q<∞ for the magnetic films.