Geodesic
On self-adjoint commuting differential operators of rank two
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 10 (2013), pp. 109-112.

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Commutativity equations for self-adjoint rank two differential operators of orders $4$ and $4g+2$ are studied in this paper. New nontrivial examples of such operators with smooth coefficients are constructed.
Keywords: commuting differential operators. 
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V. N. Davletshina. On self-adjoint commuting differential operators of rank two. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 10 (2013), pp. 109-112. http://geodesic.mathdoc.fr/item/SEMR_2013_10_a24/

[1] I. M. Krichever, “Integrirovanie nelineinykh uravnenii metodami algebraicheskoi geometrii”, Funkts. analiz i ego pril., 11:1 (1977), 15–31 | MR | Zbl

[2] I. M. Krichever, S. P. Novikov, “Golomorfnye rassloeniya nad algebraicheskimi krivymi i nelineinye uravneniya”, Uspekhi Mat. Nauk, 35:6 (1980), 47–68 | MR | Zbl

[3] O. I. Mokhov, “Kommutiruyuschie differentsialnye operatory ranga 3 i nelineinye uravneniya”, Izv. AN SSSR. Ser. matem., 53:6 (1989), 1291–1315 | MR

[4] A. E. Mironov, “Ob odnom koltse kommutiruyuschikh differentsialnykh operatorov ranga dva, otvechayuschem krivoi roda dva”, Matem. sb., 195:5 (2004), 103–114 | DOI | MR | Zbl

[5] A. E. Mironov, “Kommutiruyuschie differentsialnye operatory ranga 2, otvechayuschie krivoi roda 2”, Funkts. analiz i ego pril., 39:3 (2005), 91–94 | DOI | MR | Zbl

[6] A. E. Mironov, “O kommutiruyuschikh differentsialnykh operatorakh ranga 2”, Sibirskie elektronnye matem. izv., 6 (2009), 533–536 | MR

[7] D. Zuo, “Commuting differential operators of rank 3 associated to a curve of genus 2”, SIGMA, 8 (2012), 044 | MR

[8] I. M. Krichever, “Kommutativnye koltsa obyknovennykh lineinykh differentsialnykh operatorov”, Funkts. analiz i ego pril., 12:3 (1978), 20–31 | MR | Zbl

[9] A. E. Mironov, Self-adjoint commuting ordinary differential operators, arXiv: 1107.3356

[10] O. I. Mokhov, On commutative subalgebras of the Weyl algebra that are related to commuting operators of arbitrary rank and genus, arXiv: 1201.5979