{"paper":{"title":"Invariance of the Kaup-Kupershmidt equation and triangular auto-B\\\"acklund transformations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"nlin.SI","authors_text":"Marianna Euler, Norbert Euler","submitted_at":"2012-04-20T09:35:01Z","abstract_excerpt":"We report triangular auto-B\\\"acklund transformations for the solutions of a fifth-order evolution equation, which is a constraint for an invariance condition of the Kaup-Kupershmidt equation derived by E. G. Reyes in his paper titled \"Nonlocal symmetries and the Kaup-Kupershmidt equation\" [{\\it J. Math. Phys.} {\\bf 46}, 073507, 19 pp., 2005]. These auto-B\\\"acklund transformations can then be applied to generate solutions of the Kaup-Kupershmidt equation. We show that triangular auto-B\\\"acklund transformations result from a systematic multipotentialisation of the Kupershmidt equation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.4569","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"}