  We study the extended Bose-Hubbard model with nearest-neighbor and
next-nearest-neighbor $(V, V')$ repulsive interactions on a square lattice by
using the quantum Monte Carlo method. Unlike the case of strong $V'$ where the
ground states can be striped solids or striped supersolids, we focus on weak
$V' < V/2$ and small hoppings and find that, in the thermodynamic limit,
incommensurate solids of fractional densities varying from 1/4 to 1/2 can be
stabilized. We also show that the incommensurate solids, which are
characterized by a continuous set of wave vectors changing from $(\pi,\pi/2)$
(or $(\pi/2,\pi)$) to $(\pi,\pi)$, can be understood by a mechanism of domain
wall formation. The related ground-state phase diagram and thermal phase
transitions are also discussed.
