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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1802.00035","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-01-31T19:45:03Z","cross_cats_sorted":[],"title_canon_sha256":"1944b67fdc601d8829ed588647631ff9241c92fca48ea2d0f94bc7bc15f2f2d8","abstract_canon_sha256":"2ff3cb782bf71f783b360dffc98a0fbaf62b844de48687b6e1807de95aa09a52"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:21.791425Z","signature_b64":"sTz2e6OusK59H1YwFLAMvIgiido4Negcvv0TinHxEO/iN8ZU1T1jPTGBxXVyuigOshPQJPJi7VtPIBoudOuqBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cb70f27feb40f09e6af80f145f941c0e7acd7ef15c30ef0888b159be6bbac857","last_reissued_at":"2026-05-18T00:20:21.790895Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:21.790895Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $\\mathbb{T}$. 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