  We examine a collection of particles interacting with inverse-square two-body
potentials in the thermodynamic limit. We find explicit large-amplitude density
waves and soliton solutions for the motion of the system. Waves can be
constructed as coherent states of either solitons or phonons. Therefore, either
solitons or phonons can be considered as the fundamental excitations. The
generic wave is shown to correspond to a two-band state in the quantum
description of the system, while the limiting cases of solitons and phonons
correspond to particle and hole excitations.
