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Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2011, Volume 153, Book 3, Pages 72–80 (Mi uzku1056)  
Creation of solitons for sine-Gordon and Korteweg–de Vries equations by means of connections defining the representations of zero curvature

A. K. Rybnikov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
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Abstract: It is possible to create traveling wave type solutions (and in particular soliton solutions) of partial differential equations by means of connections defining the representations of zero curvature. In this paper we create the solitons of the sine-Gordon equation and the Korteweg–de Vries equation. In the final section we compare the proposed method for soliton creation with the inverse scattering method. We systematically use the Cartan–Laptev invariant analytic method in the work.
Keywords: connection in principal bundle, connection in associated bundle, connection defining the representation of zero curvature, differential equation, solitons, Bäcklund maps.
Received: 19.06.2011
Document Type: Article
UDC: 514.7+517.9
Language: Russian
Citation: A. K. Rybnikov, “Creation of solitons for sine-Gordon and Korteweg–de Vries equations by means of connections defining the representations of zero curvature”, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 153, no. 3, Kazan University, Kazan, 2011, 72–80
Citation in format AMSBIB
\Bibitem{Ryb11}
\by A.~K.~Rybnikov
\paper Creation of solitons for sine-Gordon and Korteweg--de~Vries equations by means of connections defining the representations of zero curvature
\serial Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki
\yr 2011
\vol 153
\issue 3
\pages 72--80
\publ Kazan University
\publaddr Kazan
\mathnet{http://mi.mathnet.ru/uzku1056}
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    		Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki
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