Gap solitons in Bose-Einstein condensates in linear and nonlinear   optical lattices
  Properties of localized states on array of BEC confined to a potential, representing superposition of linear and nonlinear optical lattices are investigated. For a shallow lattice case the coupled mode system has been derived. The modulational instability of nonlinear plane waves is analyzed. We revealed new types of gap solitons and studied their stability. For the first time a moving soliton solution has been found. Analytical predictions are confirmed by numerical simulations of the Gross-Pitaevskii equation with jointly acting linear and nonlinear periodic potentials. 
Fatkhulla Abdullaev, Abdulaziz Abdumalikov, Ravil Galimzyanov