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 Izv. Akad. Nauk SSSR Ser. Mat., 1980, Volume 44, Issue 4, Pages 805–820 (Mi izv1852)

Reduction of differential equations with symmetries

E. M. Vorob'ev

Abstract: A method for constructing group-invariant solutions of differential equations is described. At the foundation of the method lies a reduction of the dimension of the base of a bundle of $k$-jets of functions $J^k(M^n,R^1)$ by means of a passage to the manifolds of orbits of the contact action of the Lie group of partial symmetries of the differential equation. Only the orbits of a certain submanifold of $J^k(M^n,R^1)$ are considered, an extension of an involutive system of first-order differential equations associated with the action of the group.
Bibliography: 7 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1981, 17:1, 73–86

Bibliographic databases:

UDC: 517.9
MSC: Primary 35A30, 58G99; Secondary 58A20
Revised: 07.12.1979

Citation: E. M. Vorob'ev, “Reduction of differential equations with symmetries”, Izv. Akad. Nauk SSSR Ser. Mat., 44:4 (1980), 805–820; Math. USSR-Izv., 17:1 (1981), 73–86

Citation in format AMSBIB
\Bibitem{Vor80} \by E.~M.~Vorob'ev \paper Reduction of differential equations with symmetries \jour Izv. Akad. Nauk SSSR Ser. Mat. \yr 1980 \vol 44 \issue 4 \pages 805--820 \mathnet{http://mi.mathnet.ru/izv1852} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=587338} \zmath{https://zbmath.org/?q=an:0463.58014|0453.58025} \transl \jour Math. USSR-Izv. \yr 1981 \vol 17 \issue 1 \pages 73--86 \crossref{https://doi.org/10.1070/IM1981v017n01ABEH001330} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1981MW12300003}