Geodesic
Hitchin Systems on Hyperelliptic Curves
Informatics and Automation, 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{TRSPY_2020_311_a2,
     author = {P. I. Borisova and O. K. Sheinman},
     title = {Hitchin {Systems} on {Hyperelliptic} {Curves}},
     journal = {Informatics and Automation},
     pages = {27--40},
     publisher = {mathdoc},
     volume = {311},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2020_311_a2/}
}
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P. I. Borisova; O. K. Sheinman. Hitchin Systems on Hyperelliptic Curves. Informatics and Automation, Analysis and mathematical physics, Tome 311 (2020), pp. 27-40. http://geodesic.mathdoc.fr/item/TRSPY_2020_311_a2/