Spherically symmetric structural resonances self-localised in a nonlinear medium

A nonlinear self-interaction of a spherically symmetric structural resonance is considered for a homogeneous isotropic medium with a cubic nonlinearity. An induced radial-gradient distribution of the refractive index in this medium acts as a microcavity and thus ensures the existence of spherically symmetric modes. The conditions for self-localisation of a three-dimensional spherically symmetric soliton in a nonlinear medium are considered.