Zig-zag version of the Frenkel-Kontorova model

We study a generalization of the Frenkel-Kontorova model which describes a zig-zag chain of particles coupled by both the first- and second-neighbor harmonic forces and subjected to a planar substrate with a commensurate potential relief. The particles are supposed to have two degrees of freedom: longitudinal and transverse displacements. Two types of two-component kink solutions corresponding to defects with topological charges Q=±1,±2 have been treated. The topological defects with positive charge (excess of one or two particles in the chain) are shown to be immobile while the negative defects (vacancies of one or two particles) have been proved at the same parameter values to be mobile objects. In our studies we apply a minimization scheme which has been proved to be an effective numerical method for seeking solitary wave solutions in molecular systems of large complexity. The dynamics of both these types of defects has also been investigated. © 1996 The American Physical Society.