Geodesic
Commuting Differential Operators of Rank 2 with Rational Coefficients
Funkcionalʹnyj analiz i ego priloženiâ, Tome 52 (2018) no. 3, pp. 53-65

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In this paper we find new pairs of self-adjoint commuting differential operators of rank 2 with rational coefficients and prove that any curve of genus 2 written as a hyperelliptic curve is the spectral curve of a pair of commuting differential operators with rational coefficients. We also study the case where curves of genus 3 are the spectral curves of pairs of commuting differential operators of rank 2 with rational coefficients.
Keywords: integrable systems, commuting differential operators, Weyl algebra, spectral curve. 
@article{FAA_2018_52_3_a4,
     author = {V. S. Oganesyan},
     title = {Commuting {Differential} {Operators} of {Rank} 2 with {Rational} {Coefficients}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {53--65},
     publisher = {mathdoc},
     volume = {52},
     number = {3},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2018_52_3_a4/}
}
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V. S. Oganesyan. Commuting Differential Operators of Rank 2 with Rational Coefficients. Funkcionalʹnyj analiz i ego priloženiâ, Tome 52 (2018) no. 3, pp. 53-65. http://geodesic.mathdoc.fr/item/FAA_2018_52_3_a4/