  The partially attractive character of the dipole-dipole interaction leads to
phonon instability in dipolar condensates, which is followed by collapse in
three-dimensional geometries. We show that the nature of this instability is
fundamentally different in two-dimensional condensates, due to the
dipole-induced stabilization of two-dimensional bright solitons. As a
consequence, a transient gas of attractive solitons is formed, and collapse may
be avoided. In the presence of an harmonic confinement, the instability leads
to transient pattern formation followed by the creation of stable
two-dimensional solitons. This dynamics should be observable in on-going
experiments, allowing for the creation of stable two-dimensional solitons for
the first time ever in quantum gases.
