Possible soliton motion in ac-driven damped nonlinear lattices

We study the possibility of kink motion induced by pure ac driving in damped nonlinear lattices, focusing on the Frenkel-Kontorova and Toda models. Numerical simulations of the Frenkel-Kontorova model show no evidence for steady kink motion. We point out that momentum-balance in addition to energy-balance arguments are needed to understand the translation of the collective excitation. Finally, our result is discussed in view of related theoretical predictions and numerical simulations.