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Asymptotic behaviour of large-scale solutions of Hitchin’s equations in higher rank
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Let
$X$ be a compact Riemann surface. Let 
$(E,\theta )$ be a stable Higgs bundle of degree 
$0$ on 
$X$. Let 
$h_{\det (E)}$ denote a flat metric of the determinant bundle 
$\det (E)$. For any 
$t\gt 0$, there exists a unique harmonic metric 
$h_t$ of 
$(E,t\theta )$ such that 
$\det (h_t)=h_{\det (E)}$. We prove that if the Higgs bundle is induced by a line bundle on the normalization of the spectral curve, then the sequence 
$h_t$ is convergent to the naturally defined decoupled harmonic metric at the speed of the exponential order. We also obtain a uniform convergence for such a family of Higgs bundles.
