Pl. Overfelt, ON THE POSSIBILITY OF LOCALIZED WAVE-PROPAGATION USING A CLASSICAL 2-FLUID MODEL OF SUPERCONDUCTORS, Journal of mathematical physics, 35(5), 1994, pp. 2233-2258
In this paper, the classical two-fluid model for superconductors is us
ed to determine the time-dependent partial differential equations (PDE
s) which govern wave propagation in superconducting media. These equat
ions are then solved exactly in both two and three dimensions using lo
calized wave solutions rather than the traditional eigenfunction solut
ions. We have applied these localized wave solutions to the problem of
a symmetric superconducting slab, neglecting the normally conducting
current density, and found that the resultant focus wave mode magnetic
field solution expels flux from the interior of the slab and can rega
in its initial amplitude as it travels along the surface of the slab.
A comparison of the transverse part of the localized wave solution wit
h the transverse part of the more usual plane wave solution shows rema
rkable agreement.