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

The discrete Frenkel-Kontorova model, having the sine-Gordon equation as the continuous analog, was investigated numerically at a small degree of discreteness. Interaction between a kink and a breather in a discrete system was compared with the exact three-soliton solution to the continuous sine-Gordon equation. Nontrivial effects of discreteness were found numerically. One is that a kink and a breather in the discrete system are mutually attractive 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-breather binding energy EB and the maximum possible exchange energy EE for different breather frequencies omega. The results suggest that there is a threshold breather frequency for the "spontaneous" breaking up of the three-soliton oscillatory system into a kink and a breather moving in opposite directions.