Exact nonstationary solutions to the mean-field equations of motion for   two-component Bose-Einstein condensates in periodic potentials
  We study the dynamics of two-component Bose-Einstein condensates in periodic potentials in one dimension. Elliptic potentials which have the sinusoidal optical potential as a special case are considered. We construct exact nonstationary solutions to the mean-field equations of motion. Among the solutions are two types of temporally-periodic solutions -- in one type there are condensate oscillations between neighboring potential wells, while in the other the condensates oscillate from side to side within the wells. Our numerical studies of the stability of these solutions suggests the existence of one-parameter families of stable nonstationary solutions. 
R. Mark Bradley, Bernard Deconinck and J. Nathan Kutz