  We directly compare the mean-field and the many-body approach in a
one-dimensional Bose system in a harmonic trap. Both contact and dipolar
interactions are considered. We propose a multi-atom version of the phase
imprinting method to generate dark solitons in the system. We begin with a
general analysis of system dynamics and observe the emergence of a dark soliton
and a shock wave. Center of mass and soliton motion become decoupled because
the shock wave oscillates with the trap frequency and soliton does not. A
detailed investigation of frequencies reveals significant differences between
results obtained in the mean-field and the many-body pictures.
