KINKS INTERNAL-MODES IN THE FRENKEL-KONTOROVA MODEL

We consider a generalized Frenkel-Kontorova model, describing the dyna mics of a chain of particles in a periodic substrate potential, and an alyze the effect of discreteness on the existence and properties of in ternal (or shape) modes of kinks, topological excitations of the chain . In particular, we show that kink's internal modes can appear nor onl y. below but also above the phonon spectrum band and, in the latter ca se, the localized mode describes out-of-phase oscillations of the kink 's shape. For the sinusoidal on-site potential, when the model is desc ribed by the discrete sine-Gordon equation, Re reveal, in sharp contra st with the continuum limit, the existence of the kink's internal mode in a narrow region of the discreteness parameter. We apply two differ ent analytical techniques to describe the cases of weak and strong cou pling between particles, explaining qualitatively and even quantitativ ely the main features of the kink oscillations observed in numerical s imulations. We also discuss the effect of nonlinearity on the existenc e and properties of kink's internal modes and show, in particular, tha t a nonlinearity-induced frequency shift of the lattice vibrations can lend to the creation of the nonlinear kink's internal modes, which, h owever, slowly decay due to a generation of radiation through higher-o rder harmonics.