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NONLINEAR INTERACTION OF LINEAR EXCITATIONS AND THEIR LOCALIZATION AT A DEFECT IN A TWO-LEVEL SYSTEM

The features of localization of stationary states in a two-level system with nonlinear interaction at the interface of two linear media are considered. The mathematical formulation of the model is a one-dimensional boundary value problem for a linear Schrödinger equation with nonlinear boundary conditions. The conditions of localization of excitations are analyzed. It is shown that a linear localized state in a linear medium due to nonlinearity of interaction with a defect has a dispersion law, which has a characteristic feature for nonlinear waves - the dependence of energy on the degree of field amplitude.