  The motion of a dark soliton is investigated in a one-dimensional dilute
Bose-Einstein condensate confined in a harmonic trap and an optical lattice.
The harmonic trap induces a dynamical instability of the soliton, culminating
in sound emission. The presence of the optical lattice enhances the
instability, and in addition, dephases the emitted sound waves, thus preventing
stabilisation of the soliton by sound reabsorption. This instability can be
probed experimentally by monitoring the soliton oscillations under various
lattice configurations, which can be realised by changing the intensity and
angle between the laser beams that form the lattice. For short enough times,
such that the emitted sound does not reinteract with the soliton, the power
emitted by the soliton is found to be proportional to the square of the local
soliton acceleration, which is in turn proportional to the deformation of the
soliton profile.
