  We study analytically the effect of charge-neutrality breaking on the
spectrum of localized Josephson plasma waves (JPWs) in a plate of layered
superconductor of finite thickness for the case of layers parallel to the
interface. This effect results in the appearance of additional eigenmodes with
anomalous dispersion and an additional forbidden region in the spectrum of
localized modes near the Josephson plasma frequency. We consider both the
surface and waveguide eigenmodes with symmetric and anti-symmetric field
distribution with respect to the middle plane of the superconducting plate.
