{"paper":{"title":"Ground states of Nonlinear Schr\\\"{o}dinger System with Mixed Couplings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Juncheng Wei, Yuanze Wu","submitted_at":"2019-03-13T07:06:50Z","abstract_excerpt":"We consider the following $k$-coupled nonlinear Schr\\\"odinger system: \\begin{align*} \\begin{cases} &-\\Delta u_j + \\lambda_j u_j = \\mu_j u_j^3 + \\sum_{i=1, i\\not=j}^k \\beta_{i,j} u_i^2 u_j \\quad {\\rm in}\\ \\mathbb{R}^N,\\\\ &u_j>0 \\quad {\\rm in}\\ \\mathbb{R}^N, \\quad u_j(x) \\to 0 \\quad \\text{as }|x|\\to +\\infty, \\quad j=1,2,\\cdots,k, \\end{cases} \\end{align*} where $N\\leq 3$, $k\\geq3$, $\\lambda_j,\\mu_j>0$ are constants and $\\beta_{i,j}=\\beta_{j,i}\\not=0$ are parameters. There have been intensive studies for the above system when $k=2$ or the system is purely attractive ($ \\beta_{i,j}>0, \\forall i \\no"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.05340","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"}