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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2017, Volume 14, Pages 1050–1063
DOI: https://doi.org/10.17377/semi.2017.14.089 (Mi semr846) 		 
Real, complex and functional analysis

On weakly commutative triples of partial differential operators

S. P. Tsarevab, V. A. Stepanenkoa

a Siberian Federal University, pr. Svobodny, 79, 660041, Krasnoyarsk, Russia
b Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk, Russia
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DOI: https://doi.org/10.17377/semi.2017.14.089
Abstract: We investigate algebraic properties of weakly commutative triples, appearing in the theory of integrable nonlinear partial differential equations. Algebraic technique of skew fields of formal pseudodifferential operators as well as skew Ore fields of fractions are applied to this problem, relating weakly commutative triples to commuting elements of skew Ore fields of formal fractions of ordinary differential operators. A version of Burchnall–Chaundy theorem for weakly commutative triples is proved by algebraic means avoiding analytical complications typical for its proofs known in the theory of integrable equations.
Keywords: integrable systems, skew fields, formal pseudodifferential operators, Ore extensions.
Funding agency Grant number
Russian Science Foundation 14-11-00441
Received October 9, 2017, published October 19, 2017
Bibliographic databases:
Document Type: Article
UDC: 517.95
MSC: 35Q53, 37K10, 12E15
Language: Russian
Citation: S. P. Tsarev, V. A. Stepanenko, “On weakly commutative triples of partial differential operators”, Sib. Èlektron. Mat. Izv., 14 (2017), 1050–1063
Citation in format AMSBIB
\Bibitem{TsaSte17}
\by S.~P.~Tsarev, V.~A.~Stepanenko
\paper On weakly commutative triples of partial differential operators
\jour Sib. \`Elektron. Mat. Izv.
\yr 2017
\vol 14
\pages 1050--1063
\mathnet{http://mi.mathnet.ru/semr846}
\crossref{https://doi.org/10.17377/semi.2017.14.089}
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