A ug 1 99 9 The ac - Driven Motion of Dislocations in a Weakly Damped Frenkel - Kontorova Lattice

By means of numerical simulations, we demonstrate that ac field can support stably moving collective nonlinear excitations in the form of dislocations (topological solitons, or kinks) in the Frenkel-Kontorova (FK) lattice with weak friction, which was qualitatively predicted by Bonilla and Malomed [Phys. Rev. B 43, 11539 (1991)]. Direct generation of the moving dislocations turns out to be virtually impossible; however, they can be generated initially in the lattice subject to an auxiliary spatial modulation of the on-site potential strength. Gradually relaxing the modulation, we are able to get the stable moving dislocations in the uniform FK lattice with the periodic boundary conditions, provided that the driving frequency is close to the gap frequency of the linear excitations in the uniform lattice. The excitations that can be generated this way have a large and noninteger index of commensurability with the lattice (so suggesting that the actual value of the commensurability index is irrational). The simulations reveal two dif-