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We study fundamental and compound gap solitons (GSs) of matter waves inone-dimensional (1D) optical lattices (OLs) in a three-dimensional (3D)weak-radial-confinement regime, which corresponds to realistic experimentalconditions in Bose-Einstein condensates (BECs). In this regime GSs exhibitnontrivial radial structures. Associated with each 3D linear spectral bandexists a family of fundamental gap solitons that share a similar transversestructure with the Bloch waves of the corresponding linear band. GSs withembedded vorticity $m$ may exist \emph{inside} bands corresponding to othervalues of $m$. Stable GSs, both fundamental and compound ones (including vortexsolitons), are those which originate from the bands with lowest axial andradial quantum numbers. These findings suggest a scenario for the experimentalgeneration of robust GSs in 3D settings.

Three-dimensional gap solitons in Bose-Einstein condensates supported by one-dimensional optical lattices