Localization and transformation of nonlinear excitations in the vicinity of interface of media with nonlinearities of different signs

Contact states at the interface of nonlinear media with anharmonicities of different signs are considered. A model that represents a boundary-value problem for the nonlinear Schrödinger equation is proposed. Several types of stationary states that depend on energy and describe local states in the vicinity of the interface, localization of nonlinear waves passing through the interface, and transformation of such waves are obtained for the system under study. Dispersion relations that make it possible to determine the energies of such states are derived. Explicit expressions for the energies of stationary states are obtained in the limiting cases.