  We study a two-dimensional spin-orbit-coupled dipolar Bose-Einstein
condensate with repulsive contact interactions by both the variational method
and the imaginary time evolution of the Gross-Pitaevskii equation. The dipoles
are completely polarized along one direction in the 2D plane so as to provide
an effective attractive dipole-dipole interaction. We find two types of
solitons as the ground states arising from such attractive interactions: a
plane wave soliton with a spatially varying phase and a stripe soliton with a
spatially oscillating density for each component. Both types of solitons
possess smaller size and higher anisotropy than the soliton without spin-orbit
coupling. Finally, we discuss the properties of moving solitons, which are
nontrivial because of the violation of Galilean invariance.
