{"paper":{"title":"Multi-particle dynamical systems and polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.SI","authors_text":"Maria V. Demina, Nikolai A. Kudryashov","submitted_at":"2014-07-07T09:33:46Z","abstract_excerpt":"Polynomial dynamical systems describing interacting particles in the plane are studied. A method replacing integration of a polynomial multi--particle dynamical system by finding polynomial solutions of a partial differential equations is described. The method enables one to integrate a wide class of polynomial multi--particle dynamical systems. The general solutions of certain dynamical systems related to linear second--order partial differential equations are found. As a by-product of our results, new families of orthogonal polynomials are derived. Our approach is also applicable to dynamica"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.1641","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}