Kink-breather solution in the weakly discrete Frenkel-Kontorova model

The discrete Frenkel-Kontorova model, having the sine-Gordon equation as th e continuous analog, was investigated numerically at a small degree of disc reteness. Interaction between a kink and a breather in a discrete system wa s compared with the exact three-soliton solution to the continuous sine-Gor don equation. Nontrivial effects of discreteness were found numerically. On e is that a kink and a breather in the discrete system are mutually attract ive quasiparticles, so they can be regarded as a three-soliton oscillatory system. The other is the energy exchange between a kink and a breather when their collision takes place in a vicinity of a separatrix solution to the continuous sine-Gordon equation. We have estimated numerically the kink-bre ather binding energy E-B and the maximum possible exchange energy EE for di fferent breather frequencies omega The results suggest that there is a thre shold breather frequency for the "spontaneous" breaking up of the three-sol iton oscillatory system into a kink and a breather moving in opposite direc tions.