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
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.
commuting ring of differential operators, commuting two-dimensional differential operators.
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Ufa Mathematical Journal, 2011, 3:2, 89–95 (PDF, 367 kB)
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
\by A.~B.~Shabat, Z.~S.~Elkanova
\paper Commuting differential operators in two-dimension
\jour Ufimsk. Mat. Zh.
\jour Ufa Math. J.
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M. S. Akbasheva, A. B. Shabat, “Teorema o kommutirovanii v glavnom”, Ufimsk. matem. zhurn., 3:4 (2011), 3–7
F. Kh. Baichorova, Z. S. Elkanova, “Commuting differential operators of orders 4 and 6”, Ufa Math. J., 5:3 (2013), 11–19
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