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