Localized states near the interface with an internal structure between nonlinear attractive and repulsive media

We consider the nonlinear excitation localized near the media interface with an internal structure. We consider the anharmonicity of the medium characterized by a different nonlinearity on different sides of the interface. The excitations are described by nonlinear Schrödinger equation with modified short‐range interaction potential. The problem is reduced to the solution of the nonlinear Schrödinger equation with the boundary conditions of a special kind. We found the exact solutions of nonlinear Schrödinger equations satisfying the boundary conditions. We show that the existence of nonlinear localized excitations of several types is possible. They have a soliton‐like profile in the direction perpendicular to the boundary. The structure and shape of the localized states is determined by the anharmonicity parameters and the intensity of interaction of the excitations with the planar defect. We found the energy of nonlinear excitation in explicit form in special cases