Perturbation analysis of weakly discrete kinks

We present a perturbation theory of static kink solutions of discrete Klein-Gordon chains. The unperturbed solutions correspond to the kinks of the adjoint partial differential equation. The perturbation theory is based on a reformulation of the discrete chain problem into a partial differential equation with spatially modulated mass density. The first-order corrections to the kink solutions are obtained analytically and are shown to agree with exact numerical results. We use these findings to reconsider the problem of calculating the Peierls-Nabarro barrier.