{"paper":{"title":"Airy-type evolution equations on star graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.MP"],"primary_cat":"math-ph","authors_text":"Christian Seifert, Delio Mugnolo, Diego Noja","submitted_at":"2016-08-04T08:33:36Z","abstract_excerpt":"In the present paper the Airy operator on star graphs is defined and studied. The Airy operator is a third order differential operator arising in different contexts, but our main concern is related to its role as the linear part of the Korteweg-de Vries equation, usually studied on a line or a half-line. The first problem treated and solved is its correct definition, with different characterizations, as a skew-adjoint operator on a star graph, a set of lines connecting at a common vertex representing, for example, a network of branching channels. A necessary condition turns out to be that the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.01461","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"}