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We construct exact solutions of the Gross-Pitaevskii equation for solitary vortices, and approximate ones for fundamental solitons, in two-dimensional 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\"odinger equation. The VS families in the system with the attractive and repulsive nonlinearity are mutually complementary. Stable VSs with vorticity S2 and those corresponding to higher-order radial states are reported, in the case of the attraction and repulsion, respectively.
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Wu et al. (2010) studied this question.
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