Localized states near the interface with anharmonic properties between nonlinear media with different characteristics

Abstract

We consider the nonlinear excitation localized near the thin layer with nonlinear properties separated by different nonlinear media. The excitations are described by nonlinear Schrödinger equation (NLSE) with nonlinear potential. The problem is reduced to the solution of the NLSE with the boundary conditions of a special kind. We obtain the exact solutions of NLSEs satisfying the boundary conditions. We show that the existence of nonlinear localized excitations of four types is possible in a wide energy range. We derive the energy of localized excitations in the explicit form in the long-wave approximation. The conditions of localized state existence are found.