{"paper":{"title":"On the integrability of Degasperis-Procesi equation: control of the Sobolev norms and Birkhoff resonances","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Filippo Giuliani, Roberto Feola, Stefano Pasquali","submitted_at":"2018-01-31T19:45:03Z","abstract_excerpt":"We consider the dispersive Degasperis-Procesi equation $u_t-u_{x x t}-\\mathtt{c} u_{xxx}+4 \\mathtt{c} u_x-u u_{xxx}-3 u_x u_{xx}+4 u u_x=0$ with $\\mathtt{c}\\neq 0$. In \\cite{Deg} the authors proved that this equation possesses infinitely many conserved quantities. We prove that, in a neighborhood of the origin, there are infinitely many of such constants of motion which control the Sobolev norms and which are analytic in a neighborhood of the origin of some $H^s$ Sobolev space, both on $\\mathbb{R}$ and $\\mathbb{T}$. By the analysis of these conserved quantities we deduce a result of global wel"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.00035","kind":"arxiv","version":2},"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"}