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We prove the existence of orbitally stable ground states to NLS with apartial confinement together with qualitative and symmetry properties. Thisresult is obtained for nonlinearities which are $L^2$-supercritical, inparticular we cover the physically relevant cubic case. The equation that weconsider is the limit case of the cigar-shaped model in BEC.

Existence and Stability of standing waves for supercritical NLS with a Partial Confinement