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Spherically symmetric structural resonances self-localized in a Kerr-like medium

The self-action of spherically symmetric structure of electromagnetic field in a homogeneous isotropic Kerr-like medium is considered. Under certain conditions the induced spherically symmetric radially gradient distribution of refractive index acts as a microresonator, in which the effect of total internal reflection provides the existence of local spherically symmetric modes, that can be named structural resonances. The conditions of self-localization of three-dimensional spherically symmetric soliton are discussed.