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Teoreticheskaya i Matematicheskaya Fizika, 2012, Volume 171, Number 1, Pages 18–25
DOI: https://doi.org/10.4213/tmf6920 (Mi tmf6920) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Differential operators commuting in the principal part

R. A. Gabieva, A. B. Shabatb

a Aliev Karachai-Cherkess State University, Karachaevsk, Russia
b Landau Institute for Theoretical Physics, Chernogolovka, Moscow Oblast, Russia
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DOI: https://doi.org/10.4213/tmf6920
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.
Keywords: commutative ring of differential operators, Schur's formula, classification.
Received: 02.06.2011
English version:
Theoretical and Mathematical Physics, 2012, Volume 171, Issue 1, Pages 435–441
DOI: https://doi.org/10.1007/s11232-012-0042-5
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: R. A. Gabiev, A. B. Shabat, “Differential operators commuting in the principal part”, TMF, 171:1 (2012), 18–25; Theoret. and Math. Phys., 171:1 (2012), 435–441
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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