  We present results of Quantum Monte Carlo simulations for the soft core
extended bosonic Hubbard model in one dimension exhibiting the presence of
supersolid phases similar to those recently found in two dimensions. We find
that in one and two dimensions, the insulator-supersolid transition has dynamic
critical exponent z=2 whereas the first order insulator-superfluid transition
in two dimensions is replaced by a continuous transition with z=1 in one
dimension. We present evidence that this transition is in the
Kosterlitz-Thouless universality class and discuss the mechanism behind this
difference. The simultaneous presence of two types of quasi long range order
results in two soliton-like dips in the excitation spectrum.
