{"paper":{"title":"On Non-topological Solutions of the ${\\bf G}_2$ Chern-Simons System","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chang-shou Lin, Juncheng Wei, Weiwei Ao","submitted_at":"2014-03-10T19:10:23Z","abstract_excerpt":"For any rank 2 of simple Lie algebra, the relativistic Chern-Simons system has the following form: \\begin{equation}\\label{e001} \\left\\{\\begin{array}{c} \\Delta u_1+(\\sum_{i=1}^2K_{1i}e^{u_i} -\\sum_{i=1}^2\\sum_{j=1}^2e^{u_i}K_{1i}e^{u_j}K_{ij})=4\\pi\\displaystyle \\sum_{j=1}^{N_1}\\delta_{p_j}\\\\ \\Delta u_2+ (\\sum_{i=1}^2K_{2i}e^{u_i}-\\sum_{i=1}^2\\sum_{j=1}^2e^{u_i}K_{2i}e^{u_j}K_{ij})=4\\pi\\displaystyle \\sum_{j=1}^{N_2}\\delta_{q_j} \\end{array} \\right.\\mbox{in}\\; \\mathbb{R}^2, \\end{equation} where $K$ is the Cartan matrix of rank $2$. There are three Cartan matrix of rank 2: ${\\bf A}_2$, ${\\bf B}_2$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.2348","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"}