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We predict a variety of composite quiescent and spinning two- andthree-dimensional (2D and 3D) self-trapped modes in media with a repulsivenonlinearity whose local strength grows from center to periphery. These are 2Ddipoles and quadrupoles, and 3D octupoles, as well as vortex-antivortex pairsand quadruplets. Unlike other multidimensional models, where such complex boundstates either do not exist or are subject to strong instabilities, these modesare remarkably robust in the present setting. The results are obtained by meansof numerical methods and analytically, using the Thomas-Fermi approximation.The predicted states may be realized in optical and matter-wave media withcontrollable cubic nonlinearities.

Multipoles and vortex multiplets in multidimensional media with inhomogeneous defocusing nonlinearity