{"paper":{"title":"Multiple Solutions for the Non-Abelian Chern--Simons--Higgs Vortex Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gabriella Tarantello, Xiaosen Han","submitted_at":"2018-05-25T03:56:32Z","abstract_excerpt":"In this paper we study the existence of multiple solutions for the non-Abelian Chern--Simons--Higgs $(N\\times N)$-system: \\[ \\Delta u_i=\\lambda\\left(\\sum_{j=1}^N\\sum_{k=1}^N K_{kj}K_{ji}\\re^{u_j}\\re^{u_k}-\\sum_{j=1}^N K_{ji}\\re^{u_j}\\right)+4\\pi\\sum_{j=1}^{n_i}\\delta_{p_{ij}},\\quad i=1,\\dots, N; \\] over a doubly periodic domain $\\Omega$, with coupling matrix $K$ given by the Cartan matrix of $SU(N+1),$ (see \\eqref{k1} below). Here, $\\lambda>0$ is the coupling parameter, $\\delta_p$ is the Dirac measure with pole at $p$ and $n_i\\in \\mathbb{N},$ for $i=1, \\dots, N.$ When $N=1, 2$ many results are"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.09970","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"}