Modulation instability of electromagnetic excitations in the Josephson junction in a thin superconducting film

The modulation instability of plane nonlinear electromagnetic waves with finite amplitudes excited in the Josephson junction in a thin superconducting film has been studied within the framework of nonlocal electrodynamics. A dispersion equation for the increment of the wave amplitude perturbation is obtained, and the regions of the modulation instability development for the waves studied are determined. It is shown that, for the longwave amplitude perturbations, the modulation instability of these waves is developed within a finite region of wavevectors 0 <Q<Qv, while the waves with Q≥Qv are stable.