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Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, 2009, Volume 151, Book 4, Pages 93–115 (Mi uzku769)  
This article is cited in 2 scientific papers (total in 2 papers)

Bäcklund Maps in View of the Theory of Connections

A. K. Rybnikov

Faculty of Mechanics and Mathematics, M. V. Lomonosov Moscow State University
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Abstract: Study of Bäcklund transformations is one of the most interesting topics in the theory of partial differential equations. These transformations are used for searching of solutions (in particular, soliton solutions) of nonlinear equations. At the same time Bäklund transformation is the instance of differential-geometric structure generated by a differential equation.
The notion of Bäcklund transformation is a particular case of more general notion of Bäcklund map. In the present work the theory of Bäcklund maps is treated as a special chapter of the theory of connections.
Keywords: Bäcklund transformation, differential-geometric object, differential-geometric structure, connection in principal or associated bundle, connection defining the representation of zero curvature for a given partial differential equation.
Received: 15.05.2009
Document Type: Article
UDC: 514.7+517.9
Language: Russian
Citation: A. K. Rybnikov, “Bäcklund Maps in View of the Theory of Connections”, Kazan. Gos. Univ. Uchen. Zap. Ser. Fiz.-Mat. Nauki, 151, no. 4, Kazan University, Kazan, 2009, 93–115
Citation in format AMSBIB
\Bibitem{Ryb09}
\by A.~K.~Rybnikov
\paper B\"acklund Maps in View of the Theory of Connections
\serial Kazan. Gos. Univ. Uchen. Zap. Ser. Fiz.-Mat. Nauki
\yr 2009
\vol 151
\issue 4
\pages 93--115
\publ Kazan University
\publaddr Kazan
\mathnet{http://mi.mathnet.ru/uzku769}
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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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    		Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki
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