The energy of the potential relief, and of the Peierls barrier for a topological excitation (kink) in the Frenkel–Kontorova model, were calculated in the continuum limit by using second-order perturbation methods. A new technique was proposed for the analysis of this problem in the strongly discrete limit.

The Energy and Peierls Barrier of a Frenkel–Kontorova Dislocation (Kink). O.V.Usatenko, A.V.Gorbach, A.S.Kovalev: Physics of the Solid State, 2001, 43[7], 1247-51