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A collective coordinate theory is develop for soliton ratchets in the dampeddiscrete sine-Gordon model driven by a biharmonic force. An ansatz with twocollective coordinates, namely the center and the width of the soliton, isassumed as an approximated solution of the discrete non-linear equation. Theevolution of these two collective coordinates, obtained by means of theGeneralized Travelling Wave Method, explains the mechanism underlying thesoliton ratchet and captures qualitatively all the main features of thisphenomenon. The theory accounts for the existence of a non-zero depinningthreshold, the non-sinusoidal behaviour of the average velocity as a functionof the difference phase between the harmonics of the driver, the non-monotonicdependence of the average velocity on the damping and the existence ofnon-transporting regimes beyond the depinning threshold. In particular itprovides a good description of the intriguing and complex pattern of subspacescorresponding to different dynamical regimes in parameter space.

Collective Coordinates Theory for Discrete Soliton Ratchets in the sine-Gordon Model