Coupled soliton states and localization of cnoidal waves at the interface of nonlinear and linear media

Contact effects at the interface of linear and nonlinear media are studied. The problem of different stationary states in two-level system with different parameters of the dispersion relation is considered. A model that employs the nonlinear Shrödinger equation is used to show coupled states of solitons, localization of waves on one side of a defect, and transformation of nonlinear wave into linear wave upon transition through interface for the system under study due to variation in energy. Dispersion relations that determine the energies of such states are derived.