  The dynamical stability of dark solitons in dipolar Bose-Einstein condensates
is studied. For standard short-range interacting condensates dark solitons are
unstable against transverse excitations in two and three dimensions. On the
contrary, due to its non local character, the dipolar interaction allows for
stable 3D stationary dark solitons, opening a qualitatively novel scenario in
nonlinear atom optics. We discuss in detail the conditions to achieve this
stability, which demand the use of an additional optical lattice, and the
stability regimes.
