Description of Localized Josephson Plasma Waves: Legendre Functions vs WKB Approximation

Layered superconductors represent unusual materials that invoke the interest of many researchers. To describe electrodynamics in layered superconductors, well-known coupled sine-Gordon equations are widely used. The field components of the waves localized on layered superconductors in the presence of dc magnetic field can be found in WKB (quasiclassical) approximation. However, this approximation does not allow studying dispersion curves in important regions, namely near the light line and at the frequencies close to the Josephson plasma frequency. In this work, we show that the theoretical study of plasma waves localized on a layered superconductor can be performed in more accurate form using Legendre functions.