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Ufimsk. Mat. Zh., 2011, Volume 3, Issue 2, Pages 91–98 (Mi ufa97)  

This article is cited in 2 scientific papers (total in 2 papers)

Commuting differential operators in two-dimension

A. B. Shabat, Z. S. Elkanova

Aliev Karachaevo-Cherkesiya State University, Karachaevsk, Republic of Karachaevo-Cherkesiya, Russia

Abstract: A generalization to the multi-dimensional case of commutative rings of differential operators is considered. An algorithm for construction of commuting two-dimensional differential operators is formulated for a special kind of operators related to the simple one-dimensional model proposed by Burchnall and Chaundy in 1932. The problem of classifying such commutative pairs is discussed. The suggested algorithm is based on necessary conditions for general commutativity and the reducibility lemma proved in the present paper.

Keywords: commuting ring of differential operators, commuting two-dimensional differential operators.

Full text: PDF file (181 kB)
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English version:
Ufa Mathematical Journal, 2011, 3:2, 89–95 (PDF, 367 kB)

Bibliographic databases:
UDC: 517.958
Received: 10.05.2011

Citation: A. B. Shabat, Z. S. Elkanova, “Commuting differential operators in two-dimension”, Ufimsk. Mat. Zh., 3:2 (2011), 91–98; Ufa Math. J., 3:2 (2011), 89–95

Citation in format AMSBIB
\Bibitem{ShaElk11}
\by A.~B.~Shabat, Z.~S.~Elkanova
\paper Commuting differential operators in two-dimension
\jour Ufimsk. Mat. Zh.
\yr 2011
\vol 3
\issue 2
\pages 91--98
\mathnet{http://mi.mathnet.ru/ufa97}
\zmath{https://zbmath.org/?q=an:1249.13019}
\transl
\jour Ufa Math. J.
\yr 2011
\vol 3
\issue 2
\pages 89--95


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. M. S. Akbasheva, A. B. Shabat, “Teorema o kommutirovanii v glavnom”, Ufimsk. matem. zhurn., 3:4 (2011), 3–7  mathnet  zmath
    2. F. Kh. Baichorova, Z. S. Elkanova, “Commuting differential operators of orders 4 and 6”, Ufa Math. J., 5:3 (2013), 11–19  mathnet  crossref  elib
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