  We present a perturbation theory of 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 discuss the problem of calculating the Peierls-Nabarro
barrier.
