{"paper":{"title":"Formal recursion operators of integrable nonevolutionary equations and Lagrangian systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.SI","authors_text":"Agust\\'in Caparr\\'os Quintero, Rafael Hern\\'andez Heredero","submitted_at":"2018-04-12T12:15:29Z","abstract_excerpt":"We derive the general structure of the space of formal recursion operators of nonevolutionary equations~$q_{tt}=f(q,q_{x},q_t,q_{xx},q_{xt},q_{xxx},q_{xxxx})$. This allows us to classify integrable Lagrangian systems with a higher order Lagrangian of the form~$\\mathscr{L}=\\frac12 L_2(q_{xx}, q_x, q)\\,q_t^2 + L_1(q_{xx}, q_x, q)\\, q_{t} + L_0(q_{xx}, q_x, q)$. The key technique relays on exploiting a homogeneity of the determining equations of formal recursion operators. This technique allows us to extend the main results to more general equations~$q_{tt}=f(q,q_{x},\\ldots,q_{n};q_{t},q_{xt},\\ld"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.04459","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"}