  We study the soliton modes carrying fractional quantum numbers in
one-dimensional superfluids. In the $s$-wave pairing superfluid with the phase
of the order parameter twisted by opposite angles $\pm \varphi/2$ at the two
ends there is an emergent complex $Z_2$ soliton mode carrying fractional spin
number $\varphi /(2\pi)$ if there is only one pairing branch. We demonstrate
that in finite systems of length $L$, the spin density for one pairing branch
in the presence of a single soliton mode consists of two terms, a localized
spin density profile carrying fractional quantum number $\varphi/(2\pi)$, and a
uniform background $-\varphi /(2\pi L)$. The latter one vanishes in the
thermodynamic limit leaving a single soliton mode carrying fractional
excitation, however it is essential to keep the total quantum number conserved
in finite systems. This analysis is also applicable to other systems with
fractional quantum numbers, thus provides a mechanism to understand the
compatibility of the emergence of fractional charges with the integral
quantization of charges in a finite system. For the $p$-wave pairing superfluid
with the chemical potential interpolating between the strong and weak pairing
phases, the $Z_2$ soliton is associated with a Majorana zero mode. By
introducing the dimension density, we argue that the Majorana zero mode may be
understood as an object with 1/2 dimension of the single particle Hilbert
space. We conjecture a connection of the dimension density of one-dimensional
solitons with the quantum dimension of topological excitations.
