Theoretical and Mathematical Physics

, Volume 171, Issue 1, pp 435–441 | Cite as

Differential operators commuting in the principal part

Article

Abstact

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 

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Copyright information

© Pleiades Publishing, Ltd. 2012

Authors and Affiliations

  1. 1.Aliev Karachai-Cherkess State UniversityKarachaevskRussia
  2. 2.Landau Institute for Theoretical PhysicsChernogolovka, Moscow OblastRussia

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