Features of the localized states formation near a planar defect in the media with abruptly change in defocusing nonlinear response

A theoretical study of the features of the localization of fields (light beam) near a plane defect in media with a stepwise defocusing nonlinearity of the Kerr type is carried out. A one-dimensional model is used based on a generalization of the nonlinear Schrödinger equation with a point potential that simulates the interaction of excitations with a plane defect, and a nonlinear term in which the coefficients of the linear and nonlinear responses abruptly change in depending on the field amplitude in the medium. It is found two types of symmetric localized stationary states in different energy ranges. The influence of the intensity of the interaction of excitations with a defect on the profile of localization of states and the conditions for their existence is studied.