  In one-dimensional quantum systems with strong long-range repulsion particles
arrange in a quasi-periodic chain, the Wigner crystal. We demonstrate that
besides the familiar phonons, such one-dimensional Wigner crystal supports an
additional mode of elementary excitations, which can be identified with
solitons in the classical limit. We compute the corresponding excitation
spectrum and argue that the solitons have a parametrically small decay rate at
low energies. We discuss implications of our results for the behavior of the
dynamic structure factor.
