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Sibirskii Matematicheskii Zhurnal, 2002, Volume 43, Number 3, Pages 539–551 (Mi smj1310)  

This article is cited in 2 scientific papers (total in 2 papers)

Involutive distributions, invariant manifolds, and defining equations

O. V. Kaptsov

Institute of Computational Modelling, Siberian Branch of the Russian Academy of Sciences
Full-text PDF (228 kB) Citations (2)
Abstract: We introduce the notion of an invariant solution relative to an involutive distribution. We give sufficient conditions for existence of such a solution to a system of differential equations. In the case of an evolution system of partial differential equations we describe how to construct auxiliary equations for functions determining differential constraints compatible with the original system. Using this theorem, we introduce linear and quasilinear defining equations which enable us to find some classes of involutive distributions, nonclassical symmetries, and differential constraints. We present examples of reductions and exact solutions to some partial differential equations stemming from applications.
Received: 26.04.2001
English version:
Siberian Mathematical Journal, 2002, Volume 43, Issue 3, Pages 428–438
DOI: https://doi.org/10.1023/A:1015403300242
Bibliographic databases:
UDC: 517.956
Language: Russian
Citation: O. V. Kaptsov, “Involutive distributions, invariant manifolds, and defining equations”, Sibirsk. Mat. Zh., 43:3 (2002), 539–551; Siberian Math. J., 43:3 (2002), 428–438
Citation in format AMSBIB
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\by O.~V.~Kaptsov
\paper Involutive distributions, invariant manifolds, and defining equations
\jour Sibirsk. Mat. Zh.
\yr 2002
\vol 43
\issue 3
\pages 539--551
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\zmath{https://zbmath.org/?q=an:1018.58030}
\transl
\jour Siberian Math. J.
\yr 2002
\vol 43
\issue 3
\pages 428--438
\crossref{https://doi.org/10.1023/A:1015403300242}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000176346500004}
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  • https://www.mathnet.ru/eng/smj/v43/i3/p539
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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