Commuting Differential Operators of Rank 2 with Rational Coefficients

V. S. Oganesyan

Funkcionalʹnyj analiz i ego priloženiâ, Tome 52 (2018) no. 3, pp. 53-65.

Résumé

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.

Détail

Keywords: integrable systems, commuting differential operators, Weyl algebra, spectral curve.

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