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, $2Phi$, imprinted between the reservoirs. We find that the superflow never has the standard Josephson form $sim sin 2Phi $. Instead, the superflow discontinuously flips direction at $2Phi =pmpi$ 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.
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