  We analyze the dynamics of Bose-Einstein condensates loaded in rotating ring
lattices made of a few sites, and show how rotation maps the states found in
this finite system into those belonging to a static infinite lattice. Ring
currents and soliton states in the absence of a lattice find their continuation
in the presence of the lattice as nonlinear Bloch waves and soliton-like states
connecting them. Both bright gap solitons and dark-soliton trains are shown to
connect continuously to linear solutions. The existence of adiabatic paths upon
varying rotation frequency between states with quantized supercurrents suggests
highly controllable methods for the experimental generation of persistent
currents.
