Modulation instability of electromagnetic excitations in nonlocal Josephson electrodynamics of thin films of nonmagnetic and magnetic (two-and three-dimensional) superconductors

Modulation instability of nonlinear electromagnetic excitations (oscillating with the Josephson frequency) of finite amplitude is investigated in a Josephson junction in a film of a nonmagnetic, as well as of a magnetic (two-or three-dimensional), superconductor. The instability is accompanied by a nonlinear shift in frequency. Dispersion relations are derived for the time increment of small perturbations of the amplitude. It is shown that, for this type of excitations in a Josephson junction in a thin film of nonmagnetic superconductor, modulation instability develops only in a certain finite range of wave vectors, whereas in a thin film of a two-or three-dimensional magnetic superconductor it develops for any wave vector.