  We study experimentally and theoretically discrete solitons in crystalline
structures consisting of several tens of laser-cooled ions confined in a
radiofrequency trap. Resonantly exciting localized, spectrally gapped
vibrational modes of the soliton, a nonlinear mechanism leads to a
nonequilibrium steady state of the continuously cooled crystal. We find that
the propagation and the escape of the soliton out of its a
quasi-one-dimensional channel can be described as a thermal activation
mechanism. We control the effective temperature of the soliton's collective
coordinate by the amplitude of the external excitation. Furthermore, the global
trapping potential permits controlling the soliton dynamics and realizing
directed transport depending on its topological charge.
