  Longitudinal confinement of dark solitons in quasi-one-dimensional
Bose-Einstein condensates leads to sound emission and reabsorption. We perform
quantitative studies of the dynamics of a soliton oscillating in a tight dimple
trap, embedded in a weaker harmonic trap. The dimple depth provides a sensitive
handle to control the soliton-sound interaction. In the limit of no
reabsorption, the power radiated is found to be proportional to the soliton
acceleration squared. An experiment is proposed to detect sound emission as a
change in amplitude and frequency of soliton oscillations.
