Existence and Stability of Standing Waves for Supercritical NLS with a Partial Confinement

We prove the existence of orbitally stable ground states to NLS with a partial confinement together with qualitative and symmetry properties. This result is obtained for nonlinearities which are L (2)-supercritical; in particular, we cover the physically relevant cubic case. The equation that we consider is the limit case of the cigar-shaped model in BEC.