{"paper":{"title":"Infinitely many local higher symmetries without recursion operator or master symmetry: integrability of the Foursov--Burgers system revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Artur Sergyeyev","submitted_at":"2008-04-12T18:08:57Z","abstract_excerpt":"We consider the Burgers-type system studied by Foursov, w_t &=& w_{xx} + 8 w w_x + (2-4\\alpha)z z_x, z_t &=& (1-2\\alpha)z_{xx} - 4\\alpha z w_x + (4-8\\alpha)w z_x - (4+8\\alpha)w^2 z + (-2+4\\alpha)z^3, (*) for which no recursion operator or master symmetry was known so far, and prove that the system (*) admits infinitely many local generalized symmetries that are constructed using a nonlocal {\\em two-term} recursion relation rather than from a recursion operator."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0804.2020","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":""},"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"}