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On Long Waves and Solitons in Particle Lattices with Forces of Infinite Range
.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 …