Abstract
The aim of this paper is to show that the theory of jet bundles supplies the appropriate setting for the study of Bäcklund transformations. These transformations are used to solve certain partial differential equations, particularly non-linear evolution equations. Of course jets have been employed for some time in the theory of partial differential equations, but so far little use has been made of them in applications. In the meanwhile, substantial progress has been made in the study of non-linear evolution equations. This work has been encouraged by the discovery of remarkable properties of some such equations, for example the existence of soliton solutions and of infinite sequences of conservation laws. Among the techniques devised to deal with these equations are the inverse scattering method and the Bäcklund transformation. In our opinion the jet bundle formulation offers a unifying geometrical framework for understanding the properties of non-linear evolution equations and the techniques used to deal with them, although we do not consider all of these properties and techniques here.
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© 1979 D. Reidel Publishing Company, Dordrecht, Holland
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Pirani, F.A.E., Robinson, D.C., Shadwick, W.F. (1979). Introduction. In: Local Jet Bundle Formulation of Bäcklund Transformations. Mathematical Physics Studies, vol 1. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-9511-6_1
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DOI: https://doi.org/10.1007/978-94-009-9511-6_1
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-277-1036-9
Online ISBN: 978-94-009-9511-6
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