On long waves and solitons in particle lattices with forces of infinite range

Author:

Benjamin Ingimarson, Robert L. Pego

Keyword:

Nonlinear Sciences, Pattern Formation and Solitons, Pattern Formation and Solitons (nlin.PS), Analysis of PDEs (math.AP), Classical Analysis and ODEs (math.CA), Exactly Solvable and Integrable Systems (nlin.SI)

journal:

23-CNA-013

date:

2023-09-24 16:00:00

Abstract

We study waves on infinite one-dimensional lattices of particles that each interact with all others through power-law forces $F \sim r^{-p}$. 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 $p>4$, but with $2<p<4$ it is a nonlocal dispersive PDE that reduces to the Benjamin-Ono equation for $p=3$. For the infinite Calogero-Moser lattice, we find explicit formulas that describe solitary and periodic traveling waves.

PDF: On long waves and solitons in particle lattices with forces of infinite range.pdf