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TMF, 1992, Volume 92, Number 1, Pages 3–12 (Mi tmf5651)  

This article is cited in 1 scientific paper (total in 1 paper)

Symmetry algebras of linear differential equations

A. V. Shapovalova, I. V. Shirokovb

a Tomsk State University
b Omsk State University

Abstract: The local symmetries of linear differential equations are investigated by means of proven theorems on the structure of the algebra of local symmetries of translationatly and dilatationally invariant differential equations. For a nonparabolic second-order equation, the absence of nontrivial nonlinear local symmetries is proved. This means that the local symmetries reduce to the Lie algebra of linear differential symmetry operators. For the Laplace–Beltrami equation, all local symmetries reduce to the enveloping algebra of the algebra of the conformal group.

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English version:
Theoretical and Mathematical Physics, 1992, 92:1, 697–703

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Received: 29.01.1992

Citation: A. V. Shapovalov, I. V. Shirokov, “Symmetry algebras of linear differential equations”, TMF, 92:1 (1992), 3–12; Theoret. and Math. Phys., 92:1 (1992), 697–703

Citation in format AMSBIB
\Bibitem{ShaShi92}
\by A.~V.~Shapovalov, I.~V.~Shirokov
\paper Symmetry algebras of linear differential equations
\jour TMF
\yr 1992
\vol 92
\issue 1
\pages 3--12
\mathnet{http://mi.mathnet.ru/tmf5651}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1256710}
\zmath{https://zbmath.org/?q=an:0799.35013}
\transl
\jour Theoret. and Math. Phys.
\yr 1992
\vol 92
\issue 1
\pages 697--703
\crossref{https://doi.org/10.1007/BF01018697}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1992KX55000001}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. A. Drokin, A. V. Shapovalov, I. V. Shirokov, “Local symmetry algebra of Shrödinger equation for Hydrogen atom”, Theoret. and Math. Phys., 106:2 (1996), 227–236  mathnet  crossref  crossref  mathscinet  zmath  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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