This article is cited in 1 paper

Differential operators commuting in the principal part

R. A. Gabiev^a, A. B. Shabat<sup>b

a</sup> Aliev Karachai-Cherkess State University, Karachaevsk, Russia
^b Landau Institute for Theoretical Physics, Chernogolovka, Moscow Oblast, Russia

Abstract: We consider commuting differential operators with two independent variables of general form and obtain general necessary commutativity conditions for low-order operators. We show that these conditions allow classifying commuting pairs of operators whose coefficients are linear functions of the independent variables.

Keywords: commutative ring of differential operators, Schur's formula, classification.

Received: 02.06.2011

DOI: 10.4213/tmf6920

 English version: Theoretical and Mathematical Physics, 2012, 171:1, 435–441

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