Driven kinks in discrete chains: Phonon damping

Phonon radiation is shown numerically to damp the motion of a relativistically driven phi (4) soliton, even in the extremely weak discreteness limit. At higher discreteness, the soliton mobility is characterized by a discontinuous dependence on the driving force; jumps are related to phonon and breather-radiation thresholds. Moreover, the speed of a frictionless soliton cannot be lowered below a certain threshold value, or else it might get trapped between two adjacent chain sites.