{"paper":{"title":"Propagation of regularity and decay of solutions to the $k$-generalized Korteweg-de Vries equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Felipe Linares, Gustavo Ponce, Pedro Isaza","submitted_at":"2014-07-18T20:30:14Z","abstract_excerpt":"We study special regularity and decay properties of solutions to the IVP associated to the $k$-generalized KdV equations. In particular, for datum $u_0\\in H^{3/4^+}(\\mathbb R)$ whose restriction belongs to $H^l((b,\\infty))$ for some $l\\in\\mathbb Z^+$ and $b\\in \\mathbb R$ we prove that the restriction of the corresponding solution $u(\\cdot,t)$ belongs to $H^l((\\beta,\\infty))$ for any $\\beta \\in \\mathbb R$ and any $t\\in (0,T)$. Thus, this type of regularity propagates with infinite speed to its left as time evolves."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.5110","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"}