  We study the energy flow due to the motion of topological solitons in
nonlinear extended systems in the presence of damping and driving. The total
field momentum contribution to the energy flux, which reduces the soliton
motion to that of a point particle, is insufficient. We identify an additional
exchange energy flux channel mediated by the spatial and temporal inhomogeneity
of the system state. In the well-known case of a DC external force the
corresponding exchange current is shown to be small but non-zero. For the case
of AC driving forces, which lead to a soliton ratchet, the exchange energy flux
mediates the complete energy flow of the system. We also consider the case of
combination of AC and DC external forces, as well as spatial discretization
effects.
