Geodesic
Bäcklund Maps in View of the Theory of Connections
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 151 (2009) no. 4, pp. 93-115

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

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. 
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     title = {B\"acklund {Maps} in {View} of the {Theory} of {Connections}},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
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A. K. Rybnikov. Bäcklund Maps in View of the Theory of Connections. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 151 (2009) no. 4, pp. 93-115. http://geodesic.mathdoc.fr/item/UZKU_2009_151_4_a8/