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Existence and stability of standing waves for supercritical NLS with a partial confinement. (English) Zbl 1367.35150

Summary: 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.

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
35B35 Stability in context of PDEs
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