{"paper":{"title":"The Lie symmetry group of the general Lienard-type equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.DS","authors_text":"\\'Agota Figula, G\\'abor Horv\\'ath, Tam\\'as Milkovszki, Zolt\\'an Muzsnay","submitted_at":"2019-05-21T07:41:36Z","abstract_excerpt":"We consider the general Lienard-type equation $\\ddot{u} = \\sum_{k=0}^n f_k \\dot{u}^k$ for $n\\geq 4$. This equation naturally admits the Lie symmetry $\\frac{\\partial}{\\partial t}$. We completely characterize when this equation admits another Lie symmetry, and give an easily verifiable condition for this on the functions $f_0, \\dots , f_n$. Moreover, we give an equivalent characterization of this condition. Similar results have already been obtained previously in the cases $n=1$ or $n=2$. That is, this paper handles all remaining cases except for $n=3$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.08472","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"}