  We use Quantum Monte Carlo simulations to show the presence and study the
properties of solitons in the one dimensional soft-core bosonic Hubbard model
with near neighbor interaction in traps. We show that when the half-filled
Charge Density Wave (CDW) phase is doped, solitons are produced and quasi long
range order established. We discuss the implications of these results for the
presence and robustness of this solitonic phase in Bose-Einstein Condensates
(BEC) on one dimensional optical lattices in traps and study the associated
excitation spectrum. The density profile exhibits the coexistence of Mott
insulator, CDW, and superfluid regions.
