Perturbation analysis of weakly discrete kinks

TL;DR

This paper develops a perturbation theory for discrete Klein-Gordon chain kinks, providing analytical first-order corrections that match numerical results and addressing the Peierls-Nabarro barrier.

Contribution

It introduces a novel perturbation approach reformulating the discrete problem into a PDE with spatially modulated mass density, enabling analytical corrections.

Findings

First-order analytical corrections match numerical results.

Reformulation into PDE with modulated mass density.

Insights into the Peierls-Nabarro barrier calculation.

Abstract

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.