{"paper":{"title":"Partial Lie-point symmetries of differential equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"G. Cicogna, G. Gaeta","submitted_at":"2013-09-10T08:24:51Z","abstract_excerpt":"When we consider a differential equation $\\Delta=0$ whose set of solutions is ${{\\cal S}}_\\Delta$, a Lie-point exact symmetry of this is a Lie-point invertible transformation $T$ such that $T({{\\cal S}}_\\Delta)={{\\cal S}}_\\Delta$, i.e. such that any solution to $\\Delta=0$ is tranformed into a (generally, different) solution to the same equation; here we define {\\it partial} symmetries of $\\Delta=0$ as Lie-point invertible transformations $T$ such that there is a nonempty subset ${{\\cal P}} \\subset {{\\cal S}}_\\Delta$ such that $T({{\\cal P}}) = {{\\cal P}}$, i.e. such that there is a subset of so"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.2407","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"}