{"paper":{"title":"Scattering for a mass critical NLS system below the ground state with and without mass-resonance condition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Kuranosuke Nishimura, Nobu Kishimoto, Takahisa Inui","submitted_at":"2018-10-18T05:31:14Z","abstract_excerpt":"We consider a mass-critical system of nonlinear Sch\\\"{o}dinger equations \\begin{align*} \\begin{cases} i\\partial_t u +\\Delta u =\\bar{u}v,\\\\ i\\partial_t v +\\kappa \\Delta v =u^2, \\end{cases} (t,x)\\in \\mathbb{R}\\times \\mathbb{R}^4, \\end{align*} where $(u,v)$ is a $\\mathbb{C}^2$-valued unknown function and $\\kappa >0$ is a constant. If $\\kappa =1/2$, we say the equation satisfies mass-resonance condition. We are interested in the scattering problem of this equation under the condition $M(u,v)<M(\\phi ,\\psi)$, where $M(u,v)$ denotes the mass and $(\\phi ,\\psi)$ is a ground state. In the mass-resonance"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.07904","kind":"arxiv","version":3},"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"}