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arXiv · 1006.3695

Exact exact solutions of the Gross-Pitaevskii equation for stable vortex modes

Lei Wu·Lu Li·Jie-Fang Zhang·Dumitru Mihalache·Boris A. Malomed·W. M. Liu
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Abstract

We construct exact solutions of the Gross-Pitaevskii equation for solitary vortices, and approximate ones for fundamental solitons, in 2D models of Bose-Einstein condensates with a spatially modulated nonlinearity of either sign and a harmonic trapping potential. The number of vortex-soliton (VS) modes is determined by the discrete energy spectrum of a related linear Schr\"{o}dinger equation. The VS families in the system with the attractive and repulsive nonlinearity are mutually complementary. \emph{% Stable} VSs with vorticity $S\geq 2$ and those corresponding to higher-order radial states are reported for the first time, in the case of the attraction and repulsion, respectively.

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Lei Wu, Lu Li, Jie-Fang Zhang, Dumitru Mihalache, Boris A. Malomed, W. M. Liu. 2010-06-18. Exact exact solutions of the Gross-Pitaevskii equation for stable vortex modes. https://arxiv.org/abs/1006.3695

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