  We study waves on infinite one-dimensional lattices of particles that each
interact with all others through power-law forces $F \sim r^{-\beta}$. The
inverse-cube case corresponds to Calogero-Moser systems, which are well known
to be completely integrable for any finite number of particles. The formal
long-wave limit for unidirectional waves in these lattices is the Korteweg-de
Vries equation if $\beta >4$, but with $2<\beta <4$ it is a nonlocal dispersive
PDE that reduces to the Benjamin-Ono equation for $\beta=3$. For the infinite
Calogero-Moser lattice, we find explicit formulas that describe solitary and
periodic traveling waves.
