  We numerically study the imprinting and dynamics of dark solitons in a
bosonic atomic gas in a tightly-confined one-dimensional harmonic trap both
with and without an optical lattice. Quantum and thermal fluctuations are
synthesized within the truncated Wigner approximation in the quasi-condensate
description. We track the soliton coordinates and calculate position and
velocity uncertainties. We find that the phase fluctuations {\em lower} the
classically predicted soliton speed and seed instabilities. Individual runs
show interactions of solitons with sound waves, splitting and disappearing
solitons.
