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Mathematics of the USSR-Izvestiya, 1981, Volume 17, Issue 1, Pages 73–86
DOI: https://doi.org/10.1070/IM1981v017n01ABEH001330 (Mi im1852) 		 
Reduction of differential equations with symmetries

E. M. Vorob'ev
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DOI: https://doi.org/10.1070/IM1981v017n01ABEH001330
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.
Received: 17.05.1978
Revised: 07.12.1979
Russian version:
Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya, 1980, Volume 44, Issue 4, Pages 805–820
Bibliographic databases:
UDC: 517.9
MSC: Primary 35A30, 58G99; Secondary 58A20
Language: English
Original paper language: Russian
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
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\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
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\mathscinet{http://mathscinet.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{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1981MW12300003}
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  • https://doi.org/10.1070/IM1981v017n01ABEH001330
  • https://www.mathnet.ru/eng/im/v44/i4/p805
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    		Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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    Abstract page:323
    Russian version PDF:207
    English version PDF:1
    References:61
    First page:1
     
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