{"paper":{"title":"On long waves and solitons in particle lattices with forces of infinite range","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.CA","nlin.SI"],"primary_cat":"nlin.PS","authors_text":"Benjamin Ingimarson, Robert L. Pego","submitted_at":"2023-09-25T01:34:35Z","abstract_excerpt":"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 descri"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.02271","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2310.02271/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}