{"paper":{"title":"Compacton equations and integrability: the Rosenau-Hyman and Cooper-Shepard-Sodano equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.SI","authors_text":"Enrique G. Reyes, Marianna Euler, Norbert Euler, Rafael Hern\\'andez Heredero","submitted_at":"2019-04-02T08:50:29Z","abstract_excerpt":"We study integrability --in the sense of admitting recursion operators-- of two nonlinear equations which are known to possess compacton solutions: the $K(m,n)$ equation introduced by Rosenau and Hyman\n  \\[ D_t(u) + D_x(u^m) + D_x^3(u^n) = 0 \\; , \\] and the $CSS$ equation introduced by Coooper, Shepard, and Sodano,\n  \\[ D_t(u) + u^{l-2}D_x(u) + \\alpha p D_x (u^{p-1} u_x^2) + 2\\alpha D_x^2(u^p u_x) = 0 \\; . \\] We obtain a full classification of {\\em integrable $K(m,n)$ and $CSS$ equations}; we present their recursion operators, and we prove that all of them are related (via nonlocal transformat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.01291","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"}