  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.
