  We theoretically investigate superfluid properties of a one-dimensional
annular superfluid with a boost. We derive the formula of the superfluid
fraction in the one-dimensional superfluid, which was originally derived by
Leggett in the context of supersolid. We see that the superfluid fraction given
by Leggett's formula detects the emergence of solitons in the one-dimensional
annular superfluid. The formation of a bright soliton at a critical interaction
strength decreases the superfluid fraction. At a critical boost velocity, a
node appears in the soliton and the superfluid fraction vanishes. With a
transverse dimension, the soliton alters to a more localized one and it
undergoes dynamical instability at a critical transverse length. Consequently,
the superfluid fraction decreases as one increases the length up to the
critical length. With a potential barrier along the ring, the uniform density
alters to an inhomogeneous configuration and it develops a soliton localized at
one of the potential minima by increasing the interaction strength.
