The smooth distributions of the surface states in a semi-bounded medium with an abruptly change in characteristics in dependence on the field amplitude

Abstract

The wave equation with the stepwise nonlinear coefficient on the semi-axis is considered. The boundary problems allowing to obtain the exact solutions of such nonlinear wave equation are proposed. Obtained solutions describe the features of the field localization near the surface covered with fully shielding film in the medium with an abruptly change in characteristics depending on the field. Five types of the surface states with the same structure but different amplitudes, phases, characteristic localization lengths and positions of the domain boundary are found. The features of the wave distributions and the influence of control parameters such as the threshold value of the switching field, surface amplitude and their derivatives on the wave characteristics are analyzed. The change in control parameters allows us to vary the position of the domain boundary.