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Funktsional. Anal. i Prilozhen., 2018, Volume 52, Issue 3, Pages 53–65 (Mi faa3521)  

Commuting Differential Operators of Rank 2 with Rational Coefficients

V. S. Oganesyan

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: 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.

Funding Agency Grant Number
Russian Science Foundation 16-11-10260


DOI: https://doi.org/10.4213/faa3521

Full text: PDF file (185 kB)
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English version:
Functional Analysis and Its Applications, 2018, 52:3, 203–213

Bibliographic databases:

Document Type: Article
UDC: 517.926+512.77
Received: 04.09.2017

Citation: V. S. Oganesyan, “Commuting Differential Operators of Rank 2 with Rational Coefficients”, Funktsional. Anal. i Prilozhen., 52:3 (2018), 53–65; Funct. Anal. Appl., 52:3 (2018), 203–213

Citation in format AMSBIB
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