Bound states of breathers in the Frenkel-Kontorova model

In the dissipative, driven standard Frenkel-Kontorova model propagating breathers exist as attractors of the dynamics. In collisions, these excitations interact through the phonons they emit. A possible result of a two-breather collision is a bound state of two breathers. After looking at phonons and breather collisions, we present phenomenological results on breather bound states obtained from lattice dynamics simulations. In particular, we find that bound states can be characterised by the distance between the two breathers they comprise and their propagation velocity. Contrary to the single breather case, several values of the propagation velocity are easily accessible to bound states at fixed model parameters. The results are interpreted on the basis of the observed phonon spectra. The latter can easily be explained as Doppler-shifted combination frequencies of breather harmonics and a discreteness-induced perturbation frequency. Copyright EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2004