The coupled states localized near the interface between nonlinear attractive and repulsive media

We consider contact of the media with opposite signs of nonlinearity parameters. The excitations localized near the interface of two nonlinear media and propagating along it are considered. The excitations have a complex linear dispersion law with two branches. The problem is reduced to the solution of the nonlinear Schrödinger equation with boundary conditions of a special kind. We found explicit solutions of contact boundary-value problem. We show that the existence of nonlinear localized excitations of three types is possible. Dependences of the wave numbers from the system parameters for localized states are derived in explicit forms. We analyzed the conditions of existence of localized wave across the boundary.