  We investigate theoretically soliton excitations and dynamics of their
formation in strongly correlated systems of ultracold bosonic atoms in two and
three dimensional optical lattices. We derive equations of nonlinear
hydrodynamics in the regime of strong interactions and incommensurate fillings,
when atoms can be treated as hard core bosons. When parameters change in one
direction only we obtain Korteweg-de Vries type equation away from half-filling
and modified KdV equation at half-filling. We apply this general analysis to a
problem of the decay of the density step. We consider stability of one
dimensional solutions to transverse fluctuations. Our results are also relevant
for understanding nonequilibrium dynamics of lattice spin models.
