  We use Abelian Bosonization and density matrix renormalization group method
to study the effect of density on quantum phases of long range 1-D Bose-Hubbard
model. We predict the existence of supersolid phase and also other quantum
phases for this system. We have analyzed the role of long range interaction
parameter on solitonic phase near half filling. We discuss the effect of
dimerization in nearest neighbor hopping and interaction terms on the plateau
phase at the half filling.
