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Publication 23-CNA-013
Benjamin Ingimarson Robert L. Pego Abstract: We study waves on infinite one-dimensional lattices of particles that each interact with all others through power-law forces F ~ r. 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 ^{-$\beta$}$\beta$ > 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.Get the paper in its entirety as 23-CNA-013.pdf |