| We demonstrate that the recent observation of nonlinear self-trapping of matter waves in one-dimensional optical lattices [Th. Anker et al., Phys. Rev. Lett. 94, 020403 (2005)] can be associated with a novel type of broad nonlinear states existing in the gaps of the matter-wave bandgap spectrum. We find these self-trapped localized modes in one-, two-, and three dimensional periodic potentials, and demonstrate that such novel gap states can be generated experimentally in any dimension. |
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