Abstract
We present an analytical and numerical study of the nonlinear response near the lower gap of a simple system that is intercalated between two linear systems. In this finite system, the long-range interaction potential of the Kac-Baker type is taken into account in addition to the nonlinear substrate potential, which is naturally asymmetrical or has its symmetry broken by an external force. The modulated wave solutions are investigated in the weakly nonlinear case and in the small wave vector limit to calculate the gap soliton envelope and the transmissivity that presents bistability. The results in connection with the sine-Gordon system are discussed. It is shown that when the long-range interaction parameter increases, the bistability of the system tends to disappear in the cooperative short-range interactions case. Also in the competitive short-range interaction case, there are hole gap standing waves for larger values of the long-range parameter.
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