Out-of-gap Bose-Einstein solitons in optical lattices

We study the existence and the spectral and collisional properties of bright and dark solitons in a Bose-Einstein condensate (BEC) in optical lattices. Both types of these solitons are located on the background of a matter wave of finite amplitude with characteristic frequency lying outside the forbidden gap. Thus we term our solitons out-of-gap solitons. We discuss feasibility of practical preparation of the background wave to observe these solitons and make connections with recent experiments studying BEC in optical lattices. We prove that the dark out-of-gap solitons are robust against perturbations and numerically verify the possibility of their excitation using a phase imprinting technique.