Modulation instability of dispersive electromagnetic waves in a Josephson junction in a finite-thickness plate

Modulation instability of finite-amplitude dispersive electromagnetic waves is studied in the framework of nonlocal electrodynamics of a Josephson junction in a finite-thickness plate. The dispersion equation is derived for the increment of small amplitude perturbations. For this type of waves, the regions of development of modulation instability and stability of waves are determined. It is shown that modulation instability of waves develops in a finite range of wavevectors QB1(k, D, L) < Q < QB2(k, A, D, L), while waves are stable in the important long-wave region 0 ≤ Q ≤ QB1(k, D, L) and for Q ≥ QB2(k, A, D, L). The unique possibility of controlling the modulation instability region by dispersion parameter k, viz., the wave vector (or frequency ω(k)) of the modes in the linear approximation.