  Dark solitons of ultracold bosons in the vicinity of the
Mott-insulator--superfluid phase transition are studied. Making use of the
Gutzwiller ansatz we have found antisymmetric eigenstates corresponding to
standing solitons, as well as propagating solitons created by phase imprinting.
Near the phase boundary, superfluidity has either a particle or a hole
character depending on the system parameters, which greatly affects the
characteristics of both types of solitons. Within the insulating Mott regions,
soliton solutions are prohibited by lack of phase coherence between the lattice
sites. Linear and modulational stability show that the soliton solutions are
sensitive to small perturbations and, therefore, unstable. In general, their
lifetimes differ for on-site and off-site modes. For the on-site modes, there
are small areas between the Mott-insulator regions where the lifetime is very
large, and in particular much larger than that for the off-site modes.
