  The low-energy physics of (quasi)degenerate one-dimensional systems is
typically understood as the particle-like dynamics of kinks between stable,
ordered structures. Such dynamics, we show, becomes highly non-trivial when the
ground states are topologically constrained: a dynamics of the domains rather
than on the domains which the kinks separate. Motivated by recently reported
observations of charged polymers physisorbed on nanotubes, we study kinks
between helical structures of a string wrapping around a cylinder. While their
motion cannot be disentangled from domain dynamics, and energy and momentum is
not concentrated in the solitons, the dynamics of the domains can be folded
back into a one-particle picture.
