Differential operators commuting in the principal part
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.
- Publication:
-
Theoretical and Mathematical Physics
- Pub Date:
- April 2012
- DOI:
- 10.1007/s11232-012-0042-5
- Bibcode:
- 2012TMP...171..435G
- Keywords:
-
- commutative ring of differential operators;
- Schur's formula;
- classification