  We report our findings on quantum phase transitions in cold bosonic atoms in
a one dimensional optical lattice using the finite size density matrix
renormalization group method in the framework of the extended Bose-Hubbard
model. We consider wide ranges of values for the filling factors and the
nearest neighbor interactions. At commensurate fillings, we obtain two
different types of charge density wave phases and a Mott insulator phase.
However, departure from commensurate fillings yield the exotic supersolid phase
where both the crystalline and the superfluid orders coexist. In addition, we
obtain signatures for solitary waves and also superfluidity.
