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. 
J. Bellazzini, N. Boussaid, L. Jeanjean, N. Visciglia
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