Universal Localized Relaxation Mode of Uniformly Driven Kinks in Damped Multistable Systems

Linear arrays of damped multistable systems in a constant driving field $F$ are considered in the continuum limit. The existence of a universal localized relaxation mode ("inertia mode") of the driven kinks is explicitly proven. This mode, of frequency $\omega =\frac{-i\eta }{m}$, collapses in the undamped ($\eta \to 0$) free ($F\to 0$) chain into the Goldstone mode of the corresponding "free kink," and in a chain without inertia ($m\to 0$) it relaxes instantaneously.