{"paper":{"title":"Ground States of Two-Component Attractive Bose-Einstein Condensates II: Semi-trivial Limit Behavior","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Juncheng Wei, Shuai Li, Xiaoyu Zeng, Yujin Guo","submitted_at":"2017-07-24T11:51:57Z","abstract_excerpt":"As a continuation of [14], we study new pattern formations of ground states $(u_1,u_2)$ for two-component Bose-Einstein condensates (BEC) with homogeneous trapping potentials in $R^2$, where the intraspecies interaction $(-a,-b)$ and the interspecies interaction $-\\beta$ are both attractive, $i.e,$ $a$, $b$ and $\\beta$ are all positive. If $0<b<a^*:=\\|w\\|^2_2$ and $0<\\beta <a^*$ are fixed, where $w$ is the unique positive solution of $\\Delta w-w+w^3=0$ in $R^2$, the semi-trivial behavior of $(u_1,u_2)$ as $a\\nearrow a^*$ is proved in the sense that $u_1$ concentrates at a unique point and whil"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.07500","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"}