Geodesic
Hitchin Systems on Hyperelliptic Curves
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analysis and mathematical physics, Tome 311 (2020), pp. 27-40

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We describe a class of spectral curves and find explicit formulas for the Darboux coordinates of Hitchin systems corresponding to classical simple groups on hyperelliptic curves. We consider in detail the systems with rank $2$ groups on genus $2$ curves. 
@article{TM_2020_311_a2,
     author = {P. I. Borisova and O. K. Sheinman},
     title = {Hitchin {Systems} on {Hyperelliptic} {Curves}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {27--40},
     publisher = {mathdoc},
     volume = {311},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2020_311_a2/}
}
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P. I. Borisova; O. K. Sheinman. Hitchin Systems on Hyperelliptic Curves. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analysis and mathematical physics, Tome 311 (2020), pp. 27-40. http://geodesic.mathdoc.fr/item/TM_2020_311_a2/