We consider a pointlike vortex in a layered superconductor with linear
defects in the superconducting layers. We treat these defects as Jose
phson junctions with high critical current density. We consider the el
ectrodynamics of these junctions within the framework of nonlocal Jose
phson electrodynamics. We show that Josephson current through a linear
defect in a superconducting layer results in a pointlike vortex with
a superconducting core residing in this layer (Josephson pancake). We
find the mobility of a Josephson pancake. We consider a small amplitud
e wave in a Josephson junction with nonlocal electrodynamics. We treat
a bending wave for an infinite stack of Josephson pancakes. We find t
he dispersion relation for these waves. We show that their velocities
tend to a certain finite limit when the wavelength tends to infinity.