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The dynamics of Bose-Einstein condensates in optical lattices with the long-range dipole-dipole interactions, the short-range on-site interactions, and hopping terms is reduced to the generalized discrete nonlinear Schr\"odinger equation. We present the different types of solitary excitations which appear in different parameter regions. We anticipate that these excitations will be observable and discuss how the model parameters can be tuned in experiments.
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Xie et al. (2005) studied this question.
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