Internal modes in sine-Gordon chain

We address the issue of internal modes of a stable kink in a discrete sine-Gordon equation. The aim of the present study is to elucidate the effects due to the detachment of the frequency dependence of antisymmetric internal mode from the spectrum. We analyze the frequencies of the lowest modes as functions of both the number of sites and the discreteness parameter. Using a simplified approach we explain the origin of the spectrum peculiarity, which arises when the frequency dependence detaches from the quasicontinuous spectrum at some value of the intersite coupling.