{"paper":{"title":"Asymptotic dynamics for the small data weakly dispersive one-dimensional Hamiltonian ABCD system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chulkwang Kwak, Claudio Mu\\~noz","submitted_at":"2019-02-01T16:58:07Z","abstract_excerpt":"Consider the Hamiltonian $abcd$ system in one dimension, with data posed in the energy space $H^1\\times H^1$. This model, introduced by Bona, Chen and Saut, is a well-known physical generalization of the classical Boussinesq equations. The Hamiltonian case corresponds to the regime where $a,c<0$ and $b=d>0$. Under this regime, small solutions in the energy space are globally defined. A first proof of decay for this $2\\times 2$ system was given by the two authors and Poblete and Pozo, in a strongly dispersive regime, i.e. under essentially the conditions \\[ b=d > \\frac29, \\quad a,c<-\\frac1{18}."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.00454","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"}