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

We study fundamental and compound gap solitons (GSs) of matter waves in one-dimensional (1D) optical lattices (OLs) in a three-dimensional (3D) weak-radial-confinement regime, which corresponds to realistic experimental conditions in Bose-Einstein condensates (BECs). In this regime GSs exhibit nontrivial radial structures. Associated with each 3D linear spectral band exists a family of fundamental gap solitons that share a similar transverse structure with the Bloch waves of the corresponding linear band. GSs with embedded vorticity m may exist inside bands corresponding to other values of m. Stable GSs, both fundamental and compound ones (including vortex solitons), are those which originate frommore »