Existence and Stability of standing waves for supercritical NLS with a Partial Confinement (1607.00739v2)

Published 4 Jul 2016 in math.AP, math-ph, and math.MP

Abstract: 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.

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