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arXiv · 2112.09213

Self-Bound vortex states in nonlinear Schr\"odinger equations with LHY correction

Anudeep K. Arora·Christof Sparber
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Abstract

We study the cubic-quartic nonlinear Schr\"odinger equation (NLS) in two and three spatial dimension. This equation arises in the mean-field description of Bose-Einstein condensates with Lee-Huang-Yang correction. We first prove global existence of solutions in natural energy spaces which allow for the description of self-bound quantum droplets with vorticity. Existence of such droplets, described as central vortex states in 2D and 3D, is then proved using an approach via constrained energy minimizers. A natural connection to the NLS with repulsive inverse-square potential in 2D arises, leading to an orbital stability result under the corresponding flow.

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Anudeep K. Arora, Christof Sparber. 2021-12-16. Self-Bound vortex states in nonlinear Schr\"odinger equations with LHY correction. https://arxiv.org/abs/2112.09213

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