Kink ratchets in the Klein-Gordon lattice free of the Peierls-Nabarro potential

A discrete Klein-Gordon model with asymmetric potential that supports kinks free of the Peierls-Nabarro potential (PNp) is constructed. Undamped ratchet of kinks under harmonic AC driving force is investigated in this model numerically and contrasted with the kink ratchets in the conventional discrete model where kinks experience the PNp. We show that the PNp-free kinks exhibit ratchet dynamics very much different from that reported for the conventional lattice kinks which experience PNp [see, e.g., Phys. Rev. E {\bf 73}, 066621 (2006)]. Particularly, we could not observe any significant influence of the discreteness parameter on the acceleration of PNp-free kinks induced by the AC driving.