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Directed motion of topological solitons (kinks or antikinks) in the dampedand AC-driven discrete sine-Gordon system is investigated. We show that if thedriving field breaks certain time-space symmetries, the soliton can performunidirectional motion. The phenomenon resembles the well known effects ofratchet transport and nonlinear harmonic mixing. Direction of the motion andits velocity depends on the shape of the AC drive. Necessary conditions for theoccurrence of the effect are formulated. In comparison with the previouslystudied continuum case, the discrete case shows a number of new features:non-zero depinning threshold for the driving amplitude, locking to the rationalfractions of the driving frequency, and diffusive ratchet motion in the case ofweak intersite coupling.Comment: 13 pages, 13 figure

Discrete soliton ratchets driven by biharmonic fields