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Mathematics of the USSR-Sbornik, 1989, Volume 64, Issue 2, Pages 427–441
DOI: https://doi.org/10.1070/SM1989v064n02ABEH003318 (Mi sm1752) 		 
This article is cited in 106 scientific papers (total in 106 papers)

Approximate symmetries

V. A. Baikov, R. K. Gazizov, N. Kh. Ibragimov
English version PDF (688 kB) Citations (106) Russian version article
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DOI: https://doi.org/10.1070/SM1989v064n02ABEH003318
Abstract: A theory, based on the new concept of an approximate group, is developed for approximate group analysis of differential equations with a small parameter. An approximate Lie theorem is proved that enables one to construct approximate symmetries that are stable under small perturbations of the differential equations. The use of the algorithm is illustrated in detail by examples: approximate symmetries of nonlinear wave equations are considered along with a broad class of evolution equations that includes the Korteweg–de Vries and Burgers–Korteweg–de Vries equations.
Tables: 2.
Bibliography: 4 titles.
Received: 20.04.1987
Bibliographic databases:
UDC: 517.958
MSC: Primary 58F37, 58G37, 35A30, 34A10; Secondary 35K22, 35Q20, 58G35
Language: English
Original paper language: Russian
Citation: V. A. Baikov, R. K. Gazizov, N. Kh. Ibragimov, “Approximate symmetries”, Math. USSR-Sb., 64:2 (1989), 427–441
Citation in format AMSBIB
\Bibitem{BaiGazIbr88}
\by V.~A.~Baikov, R.~K.~Gazizov, N.~Kh.~Ibragimov
\paper Approximate symmetries
\jour Math. USSR-Sb.
\yr 1989
\vol 64
\issue 2
\pages 427--441
\mathnet{http://mi.mathnet.ru//eng/sm1752}
\crossref{https://doi.org/10.1070/SM1989v064n02ABEH003318}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=965885}
\zmath{https://zbmath.org/?q=an:0683.35004}
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    • This publication is cited in the following 106 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics
     
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