  A model of a Bose-Einstein condensate in a ring optical lattice with atomic
dissipations applied at a stationary or at a moving location on the ring is
presented. The localized dissipation is shown to generate and stabilize both
stationary and traveling lattice solitons. Among many localized solutions, we
have generated spatially stationary quasiperiodic lattice soltions and a family
of traveling lattice solitons with two intensity peaks per potential well with
no counterpart in the discrete case. Collisions between traveling and
stationary lattice solitons as well as between two traveling lattice solitons
display a critical dependence from the lattice depth. Stable counterpropagating
solitons in ring lattices can find applications in gyroscope interferometers
with ultra-cold gases.
