Abstract
In this paper we address the question of the survival of metastable structures as steady states of the dissipative dynamics of the Frenkel-Kontorova model. For constant driving force the answer is negative as a consequence of the asymptotic uniqueness of the steady state. On the contrary, when the system is driven by periodic external forces, synchronization to the frequency of the force sustains under some conditions the stable motion of metastable structures. Plausibility arguments leading to this conclusion are confirmed by numerical results on several types of metastable structures. We discuss the applicability of these results to models for charge-density-wave dynamics and Josephson-junction arrays.
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