Soliton ratchetlike dynamics by ac forces with harmonic mixing

The possibility of unidirectional motion of a kink (topological soliton) of a dissipative sine-Gordon equation in the presence of ac forces with harmonic mixing (at least biharmonic) and of zero mean, is presented. The dependence of the kink mean velocity on system parameters is investigated numerically and the results are compared with a perturbation analysis based on a point-particle representation of the soliton. We find that first order perturbative calculations lead to incomplete descriptions, due to the important role played by the soliton-phonon interaction in establishing the phenomenon. The role played by the temporal symmetry of the system in establishing soliton dc motions that resemble usual soliton ratchets, is also emphasized. In particular, we show the existence of an asymmetric internal mode on the kink profile that couples to the kink translational mode through the damping in the system. Effective soliton transport is achieved when the internal mode and the external force get phase locked. We find that for kinks driven by biharmonic drivers consisting of the superposition of a fundamental driver with its first odd harmonic, the transport arises only due to this internal mode mechanism, while for biharmonic drivers with even harmonic superposition, also a point-particle contribution to the drift velocity is present. The phenomenon is robust enough to survive the presence of thermal noise in the system and can lead to several interesting physical applications.