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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","authors_text":"Jun Yang, Lipeng Duan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-05-01T15:27:48Z","title":"On the non-degeneracy of radial vortex solutions for a coupled Ginzburg-Landau 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