A diversity of localised solutions of the one-dimensional nonlinear Schrödinger (NLS) equation with a periodic potential is found. Among them are bright and dark solitons and complex coupled solitary waves. These objects have been found by analysing a discrete dynamical system associated with this equation. Direct numerical integrations of the NLS system show that some of these solutions can be dynamically stable. The possibility to observe these solutions in real experiments is also briefly discussed.
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Alfimov et al. (2002) studied this question.
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