Article
Ufa Mathematical Journal
Volume 3, Number 2, pp. 89-95
Commuting differential operators in two-dimension
Elkanova Z.S., Shabat A.B.
Download PDF
Article on MathNetAbstact
A generalization to the multi-dimensional case of commutative rings of differential operators is considered. For a special kind of operators related with the simple one-dimensional model proposed by Burchnall and Chaundy in 1932, an algorithm is formulated for the construction of commuting two-dimensional differential operators. The problem of classifying such commutative pairs is discussed. The algorithm uses the following results proved here: necessary conditions for general commutativity, and a reducibility lemma.