A Family of Solitary Waves in Frenkel-Kontorova Lattice

TL;DR

This paper constructs a family of solitary waves in the Frenkel-Kontorova lattice and its approximations, characterizing their profiles and relation to dislocation motion, advancing understanding of nonlinear wave phenomena in discrete systems.

Contribution

It introduces a new family of solitary waves in the Frenkel-Kontorova model, detailing their profiles and dynamics, including continuum and quasi-continuum approximations.

Findings

Solitary waves characterized by local maxima in their profiles.

Relation established between external force and wave velocity.

Waves interpreted as coherent motion of dislocation pairs.

Abstract

A family of solitary waves is constructed in Frenkel-Kontorova model and its continuum and quasi-continuum approximations. Each solitary waves is characterised by the number of local maxima in its profile and a relation between external force and the velocity of wave. Such waves may be interpreted as a coherent motion, with constant velocity, of two dislocations of opposite sign or of kink-antikink pair.