Algebraic bright and vortex solitons in defocusing media
  We demonstrate that spatially inhomogeneous defocusing nonlinear landscapes with the nonlinearity coefficient growing toward the periphery as [1+abs(r)]**a support one- and two-dimensional fundamental and higher-order bright solitons, as well as vortex solitons, with algebraically decaying tails. The energy flow of the solitons converges as long as nonlinearity growth rate exceeds the dimensionality, i.e., a>D. Fundamental solitons are always stable, while multipoles and vortices are stable if the nonlinearity growth rate is large enough. 
Olga V. Borovkova, Yaroslav V. Kartashov, Boris A. Malomed, Lluis   Torner
physics.optics cond-mat.quant-gas nlin.PS