The nonlinear localized electromagnetic modes in a plate of layered superconductor are studied theoretically. The plate is assumed to be embedded in a uniform dielectric environment, the superconducting layers are perpendicular to the surface of the plate, and the modes propagate across the layers. Despite the symmetry of the system, the symmetric and anti-symmetric, as well as nonsymmetric with respect to the magnetic field, localized modes can exist in the plate, that is due to the nonlinearity of the Josephson plasma. It is shown that under certain conditions the dispersion of localized modes can be anomalous, and the group velocity can vanish. By virtue of the nonlinearity, the dispersion relations contain the amplitude of the localized mode, that makes it possible to ob-serve the stop-light phenomenon of localized modes in the plate of the layered superconductor.
PACS: 74.72.–h Cuprate superconductors; PACS: 73.20.Mf Collective excitations (including excitons, polarons, plasmons and other charge-density excitations); PACS: 52.35.Mw Nonlinear phenomena: waves, wave propagation, and other interactions.