  In this paper, we explore the persistent current in thin superconducting
wires and accurately examine the effects of the phase slips on that current.
The main result of the paper is the formula for persistent current in terms of
the solutions of certain (nonlinear) integral equation. This equation allows to
find asymptotics of the current at long(small) length of the wire, in that
paper, we interested in the region in which the system becomes strongly
interacting and very few amounts of information can be extracted by
perturbation theory. Nevertheless, due to the integrability, exact results for
the current can be obtained. We observe that at the limit of a long wire, the
current becomes exponentially small, we believe that it is the signal that
phase slips may destroy superconductivity for long wires, below BKT phase
transition.
