{"paper":{"title":"$H^1$-scattering for systems of $N$-defocusing weakly coupled NLS equations in low space dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Biagio Cassano, Mirko Tarulli","submitted_at":"2014-09-30T08:00:49Z","abstract_excerpt":"We prove that the scattering operators and wave operators are well-defined in the energy space for the system of defocusing Schr\\\"odinger equations\n  $$ \\begin{cases} i\\partial_t u_\\mu + \\Delta u_\\mu - \\sum_{\\mu,\\nu=1 }^N \\beta_{\\mu\\nu}|u_\\nu|^{p+1}|u_\\mu|^{p-1}u_\\mu=0, \\quad\\quad \\mu=1,\\dots,N,\\\\(u_\\mu(0,\\cdot))_{\\mu=1}^N= (u_{\\mu,0})_{\\mu=1}^N \\in H^1(\\mathbb R^d)^N. \\end{cases} $$ with $N\\geq 2$, $\\beta_{\\mu\\nu} \\geq 0$, $\\beta_{\\mu\\mu}\\neq 0$ for $p>2 $ if $d=1$, $p>1 $ if $d=2$ and $ 1 \\leq p < 2$ if $d=3$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.8416","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"}