Effect of damping on kink ratchets in the Klein-Gordon lattice free of the Peierls-Nabarro potential

Ratchet of kink under harmonic ac driving force in the discrete Klein-Gordon model with asymmetric potential and with a damping term is investigated numerically. A particular feature of the considered discrete model is that supported kinks are free of the Peierls-Nabarro potential (PNp). It is demonstrated that, depending on the strength of damping, the drift velocity of the kink can be positive (weak damping) or negative (strong damping). The absence of PNp results in a weak dependence of kink drift velocity on the discreteness parameter.