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

TL;DR

This paper proves the existence and stability of ground states for a supercritical nonlinear Schrödinger equation with partial confinement, relevant to Bose-Einstein condensates, including the physically important cubic case.

Contribution

It establishes the existence and orbital stability of ground states for supercritical NLS with partial confinement, covering the cubic case and related physical models.

Findings

Existence of orbitally stable ground states for supercritical NLS with partial confinement.

Qualitative and symmetry properties of these ground states.

Relevance to the cigar-shaped Bose-Einstein condensate model.

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.