  The nonequilibrium quantum dynamics of few boson ensembles which experience a
spatially modulated interaction strength and are confined in finite optical
lattices is investigated. We utilize a cosinusoidal spatially modulated
effective interaction strength which is characterized by its wavevector,
inhomogeneity amplitude, interaction offset and a phase. Performing quenches
either on the wavevector or the phase of the interaction profile an enhanced
imbalance of the interatomic repulsion between distinct spatial regions of the
lattice is induced. Following both quench protocols triggers various tunneling
channels and a rich excitation dynamics consisting of a breathing and a cradle
mode. All modes are shown to be amplified for increasing inhomogeneity
amplitude of the interaction strength. Especially the phase quench induces a
directional transport enabling us to discern energetically, otherwise,
degenerate tunneling pathways. Moreover, a periodic population transfer between
distinct momenta for quenches of increasing wavevector is observed, while a
directed occupation of higher momenta can be achieved following a phase quench.
Finally, during the evolution regions of partial coherence are revealed between
the predominantly occupied wells.
