Localization in a symmetric three-layer structure consisting of a defocusing layer with focusing covers separated by interfaces with a nonlinear response

The peculiarities of stationary state localization in a symmetric three-layer structure, in which the inner layer is characterized by a defocusing Kerr nonlinearity, and the outer plates are focused, are considered. Nonlinear Schr$\"o$dinger equation with a nonlinear self-consistent potential was used to describe the localization of the field near the interfaces with a nonlinear response. It is shown that a localized state exists with an antisymmetric distribution of the field profile relative to the middle of the inner layer. The energies of stationary localized states are found in an explicit analytic form and the conditions for their existence are analyzed.