{"paper":{"title":"On the non-degeneracy of radial vortex solutions for a coupled Ginzburg-Landau system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jun Yang, Lipeng Duan","submitted_at":"2019-05-01T15:27:48Z","abstract_excerpt":"For the following Ginzburg-Landau system in ${\\mathbb R}^2$\n  \\begin{align*}\n  \\begin{cases}\n  -\\Delta w^+ +\\Big[A_+\\big(|w^+|^2-{t^+}^2\\big)+B\\big(|w^-|^2-{t^-}^2\\big)\\Big]w^+=0,\n  \\\\[3mm] -\\Delta w^- +\\Big[A_-\\big(|w^-|^2-{t^-}^2\\big)+B\\big(|w^+|^2-{t^+}^2\\big)\\Big]w^-=0, \\end{cases} \\end{align*} with constraints $ A_+, A_->0$, $B<0$, $B^2<A_+A_-$ and $t^+, t^->0$, we will concern its linearized operator ${\\mathcal L}$ around the radially symmetric solution $w(x)=(w^+, w^-): {\\mathbb R}^2 \\rightarrow\\mathbb{C}^2$ of degree pair $(1, 1)$ and prove the non-degeneracy result: the kernel of ${\\m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.00347","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"}