It was demonstrated, by means of numerical simulation, that an alternating-current field could support stably-moving collective non-linear excitations in the form of dislocations, topological solitons, or kinks in a Frenkel-Kontorova lattice with weak friction. Direct generation of moving dislocations was found to be essentially impossible, but they could be initially generated in a lattice which was subjected to an auxiliary spatial modulation of the on-site potential strength. By gradually relaxing the modulation, it was possible to obtain stable moving dislocations in a uniform Frenkel-Kontorova lattice with periodic boundary conditions; provided that the driving frequency was close to the gap frequency of linear excitations in the uniform lattice. The excitations which could be generated in this way had a large and non-integer index of commensurability with respect to the lattice. This suggested that the actual value of the commensurability index was irrational. The simulations revealed 2 different types of moving dislocation. These were broad ones which extended to roughly 50% of the full length of the periodic lattice (and could not be termed solitons), and localized soliton-like dislocations which could be found in an excited state and exhibited strong persistent internal vibrations. The threshold amplitude of the driving force which was necessary in order to support the travelling excitation was found as a function of the friction coefficient. Its extrapolation suggested that the threshold did not vanish at zero friction, and this was explained in terms of radiation losses. The moving dislocation could be observed experimentally in an array of coupled small Josephson junctions in the form of an inverse Josephson effect. That is, a direct-current voltage response to a uniformly applied alternating-current bias.

The Alternating-Current Driven Motion of Dislocations in a Weakly Damped Frenkel-Kontorova Lattice. G.Filatrella, B.A.Malomed: Journal of Physics - Condensed Matter, 1999, 11[37], 7103-14