SYMMETRICAL LOCALIZED STATE IN THE SIMPLEST MODEL OF NONLINEAR MEDIUM WITH A POINT DEFECT

The model of the stepwise nonlinearity is used to a theoretical description of the features of localized excitations near a point defect. The problem consists of the one-dimensional stationary Schrodinger equation with the nonlinear term stepwise depending on the field and a delta-function potential. The presence of nonlinearity leads to the fact that a bound state can exist in a potential well of finite depth. The comparison of the localized states described by the simplest stepwise nonlinearity and Kerr nonlinearity models is made. It is found that a narrower localization of the field near the defect is characteristic to the model with the simplest stepwise nonlinearity.