Localization on the interface with nonlinear response between linear and nonlinear focusing media

The nonlinear excitations near the thin layer with nonlinear properties separated linear and media with Kerr-type focusing (positive) nonlinearity are considered. The nonlinear Schrödinger equation with nonlinear potential containing the two parameters describes the new type nonlinear excitations. The problem is reduced to the solution of linear and nonlinear Schrödinger equations on half spaces with the nonlinear boundary conditions at the interface plane. The new two type nonlinear excitations describing the blocking effect of the field passed through the interface into a linear half-space from nonlinear one are obtained and analyzed. The exact energy levels of excitations of special kind and in explicit form in the long-wave approximation are derived. The conditions of excitation existence in dependence on the interface and media characteristics are found.