A Solution to the Frenkel-Kontorova Dislocation Model

Abstract

An exact solution to the nonlinear difference equation which describes a static configuration in the Frenkel-Kontorova dislocation model is given. The solution is in terms of a power series which is proved convergent. Previously, only approximate solutions had been obtained by replacing the difference equation by a differential equation. A numerical comparison is made between the exact and the approximate solutions and the Peierls energies they give.