Lobachevskii Journal of Mathematics
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Lobachevskii Journal of Mathematics, 2006, Volume 23, Pages 57–70 (Mi ljm17)  
This article is cited in 2 scientific papers (total in 2 papers)

Note on two compatibility criteria: Jacobi–Mayer bracket vs. differential Gröbner basis

B. S. Kruglikov

University of Tromsø
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Abstract: We compare two compatibility criteria for overdetermined PDEs: one via geometric theory of differential equations and another via differential algebra approach. Whenever both are applicable, we show that the former is more effective, though in some very special cases they are equivalent.
Keywords: compatibility of differential equations, Jacobi bracket, Mayer bracket, differential Gröbner basis, Kolchin–Ritt algorithm.
Submitted by: V. V. Lychagin
Received: 27.05.2006
Bibliographic databases:
Language: English
Citation: B. S. Kruglikov, “Note on two compatibility criteria: Jacobi–Mayer bracket vs. differential Gröbner basis”, Lobachevskii J. Math., 23 (2006), 57–70
Citation in format AMSBIB
\Bibitem{Kru06}
\by B.~S.~Kruglikov
\paper Note on two compatibility criteria: Jacobi--Mayer bracket vs.\ differential Gr\"obner basis
\jour Lobachevskii J. Math.
\yr 2006
\vol 23
\pages 57--70
\mathnet{http://mi.mathnet.ru/ljm17}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2293365}
\zmath{https://zbmath.org/?q=an:1117.35053}
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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