  We study a flow of ultracold bosonic atoms through a one-dimensional channel
that connects two macroscopic three-dimensional reservoirs of Bose-condensed
atoms via weak links implemented as potential barriers between each of the
reservoirs and the channel. We consider reservoirs at equal chemical potentials
so that a superflow of the quasi-condensate through the channel is driven
purely by a phase difference, $2\Phi$, imprinted between the reservoirs. We
find that the superflow never has the standard Josephson form $\sim \sin 2\Phi
$. Instead, the superflow discontinuously flips direction at $2\Phi =\pm\pi$
and has metastable branches. We show that these features are robust and not
smeared by fluctuations or phase slips. We describe a possible experimental
setup for observing these phenomena.
