  We extend our previous work on soliton ratchet devices [L. Morales-Molina et
al., Eur. Phys. J. B 37, 79 (2004)] to consider the joint effect of two ac
forces including non-harmonic drivings, as proposed for particle ratchets by
Savele'v et al. [Europhys. Lett. 67}, 179 (2004); Phys. Rev. E {\bf 70} 066109
(2004)]. Current reversals due to the interplay between the phases, frequencies
and amplitudes of the harmonics are obtained. An analysis of the effect of the
damping coefficient on the dynamics is presented. We show that solitons give
rise to non-trivial differences in the phenomenology reported for particle
systems that arise from their extended character. A comparison with soliton
ratchets in homogeneous systems with biharmonic forces is also presented. This
ratchet device may be an ideal candidate for Josephson junction ratchets with
intrinsic large damping.
