{"paper":{"title":"Classification of Integrable Evolution Equations of the Form $u_t=u_{xxx}+f(t,x,u,u_x,u_{xx})$","license":"","headline":"","cross_cats":["nlin.SI"],"primary_cat":"solv-int","authors_text":"Ayse Humeyra Bilge","submitted_at":"1996-05-17T11:59:11Z","abstract_excerpt":"We obtain the classification of integrable equations of the form $u_t=u_{xxx}+f(t,x,u,u_x,u_{xx})$ using the formal symmetry method of Mikhailov et al [A.V.Mikhailov, A.B.Shabat and V.V.Sokolov, in {\\it What is Integrability} edited by V.E. Zakharov (Springer-Verlag, Berlin 1991)]. We show that all such equations can be transformed to an integrable equation of the form $v_t=v_{xxx}+f(v,v_x,v_{xx})$ using transformations $\\Phi(x,t,u,v,u_x,v_x)=0$, and the $u_{xx}$ dependence can be eliminated except for two equations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"solv-int/9605004","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/solv-int/9605004/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}