Localized states near a thin layer with the nonlinear properties separating nonlinear focusing and defocusing media

Based on the nonlinear Schrödinger equation, new types of localized states near the contact of defocusing and self-focusing media with the Kerr nonlinearity separated by a thin defect layer with the similar nonlinearity have been described. The occurrence of the localized states of two types is demonstrated. The dispersion relations between the excitation localization energy and characteristics of the media and defect layer have been obtained. The localization energy levels for particular cases have been obtained in the explicit analytical form.