Generation and annihilation of dislocations in the discrete Frenkel-Kontorova model

The collision between two breathers and between a breather and a kink has been studied in the one-dimensional Frenkel-Kontorova model with a small degree of discreteness. The range of quasiparticle parameters, for which the collision is accompanied by a conversion of energy from kinetic to potential form or conversely was found. The energy conversion can under certain circumstances lead to the break-up of breathers into kink-antikink pairs. In the frame of the considered model they represent dislocation loops or pairs of jogs or kinks in dislocations. Under time reversed conditions the fusion of kink-antikink pairs into breathers may be considered. A condition for the inelastic interaction of quasiparticles was found.