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We study the properties of the ground state of Nonlinear Schr\"odingerEquations with spatially inhomogeneous interactions and show that itexperiences a strong localization on the spatial region where the interactionsvanish. At the same time, tunneling to regions with positive values of theinteractions is strongly supressed by the nonlinear interactions and as thenumber of particles is increased it saturates in the region of finiteinteraction values. The chemical potential has a cutoff value in these systemsand thus takes values on a finite interval. The applicability of the phenomenonto Bose-Einstein condensates is discussed in detail.

physica d nonlinear phenomena

Localization phenomena in Nonlinear Schrodinger equations with spatially  inhomogeneous nonlinearities: Theory and applications to Bose-Einstein  condensates