Theoretical and Mathematical Physics

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

Differential operators commuting in the principal part

  • R. A. Gabiev
  • A. B. Shabat


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.


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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