{"paper":{"title":"Scattering for a 3D coupled nonlinear Schr\\\"odinger system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ademir Pastor, Luiz Gustavo Farah","submitted_at":"2016-03-17T23:02:06Z","abstract_excerpt":"We consider the three-dimensional cubic nonlinear Schr\\\"odinger system\n  \\begin{equation*} \\begin{cases} i\\partial_tu+\\Delta u+(|u|^2+\\beta |v|^2)u=0,\\\\ i\\partial_tv+\\Delta v+(|v|^2+\\beta |u|^2)v=0. \\end{cases} \\end{equation*} Let $(P,Q)$ be any ground state solution of the above Schr\\\"odinger system. We show that for any initial data $(u_0,v_0)$ in $H^1(\\mathbb{R}^3)\\times H^1(\\mathbb{R}^3)$ satisfying $M(u_0,v_0)A(u_0,v_0)<M(P,Q)A(P,Q)$ and $M(u_0,v_0)E(u_0,v_0)<M(P,Q)E(P,Q)$, where $M(u,v)$ and $E(u,v)$ are the mass and energy (invariant quantities) associated to the system, the correspondi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.05723","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"}