  We explore stability regions for solitons in the nonlinear Schrodinger
equation with a spatially confined region carrying a combination of
self-focusing cubic and septimal terms, with a quintic one of either focusing
or defocusing sign. This setting can be implemented in optical waveguides based
on colloids of nanoparticles. The solitons stability is identified by solving
linearized equations for small perturbations, and is found to fully comply with
the Vakhitov-Kolokolov criterion. In the limit case of tight confinement of the
nonlinearity, results are obtained in an analytical form, approximating the
confinement profile by a delta-function. It is found that the confinement
greatly increases the largest total power of stable solitons, in the case when
the quintic term is defocusing, which suggests a possibility to create tightly
confined high-power light beams guided by the spatial modulation of the local
nonlinearity strength.
