Abstract
The nonlinear dynamics of systems with a spatially periodic ground state was studied. The dynamics of kinks against the background of a periodic soliton structure was considered for the example of the sine-Klein-Gordon model that described a fluxon lattice in a long Josephson contact in an external magnetic field and an incommensurate structure of a surface atomic layer or adatom chains on the surface of a crystal. The velocity of moving kinks was shown to be bounded from above and from below if the ground state was spatially periodic.
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