  The stacks of Bose-Einstein condensates coupled by long Josephson junctions
present a rich phenomenology feasible to experimental realization and specially
suitable for technological applications as the nonlinear-optics and
superconducting analogues have already proved. Among this, we show that
transverse Bloch waves excited in arrays of one-dimensional coupled condensates
can carry tunneling superflows whose dynamical stability depends on the
quasimomentum. Across the stacks with periodic boundary conditions, forming
closed ring-shaped systems, such Bloch states yield transverse Josephson
vortices with a generic non-integer circulation in units of $h/m$.
Additionally, the superpositions of degenerate linear Bloch waves can suppress
the supercurrents and give rise to families of nonlinear standing-wave states
with strong (transverse) spatial localization. Stable states of this type can
also be found in finite size systems.
