{"paper":{"title":"On a two-component Bose-Einstein condensate with steep potential wells","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Tsung-fang Wu, Wenming Zou, Yuanze Wu","submitted_at":"2014-12-26T02:20:23Z","abstract_excerpt":"In this paper, we study the following two-component systems of nonlinear Schr\\\"odinger equations \\begin{equation*} \\left\\{\\aligned&\\Delta u-(\\lambda a(x)+a_0(x))u+\\mu_1u^3+\\beta v^2u=0\\quad&\\text{in }\\bbr^3,\\\\ &\\Delta v-(\\lambda b(x)+b_0(x))v+\\mu_2v^3+\\beta u^2v=0\\quad&\\text{in }\\bbr^3,\\\\ &u,v\\in\\h,\\quad u,v>0\\quad\\text{in }\\bbr^3,\\endaligned\\right. \\end{equation*} where $\\lambda,\\mu_1,\\mu_2>0$ and $\\beta<0$ are parameters; $a(x), b(x)\\geq0$ are steep potentials and $a_0(x),b_0(x)$ are sign-changing weight functions; $a(x)$, $b(x)$, $a_0(x)$ and $b_0(x)$ are not necessarily to be radial symmet"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.7881","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"}