  We study the dynamics of magnetic domain walls in the Peierls potential due
to the discreteness of the crystal lattice. The propagation of a narrow domain
wall (comparable to the lattice parameter) under the effect of a magnetic field
proceeds through the formation of kinks in its profile. We predict that,
despite the discreteness of the system, such kinks can behave like sine-Gordon
solitons in thin films of materials such as yttrium iron garnets, and we derive
general conditions for other materials. In our simulations we also observe
long-lived breathers. We provide analytical expressions for the effective mass
and limiting velocity of the kink in excellent agreement with our numerical
results.

Mesoscale and Nanoscale Physics;Materials Science