Titlebook: Local Jet Bundle Formulation of Bäckland Transformations; With Applications to F. A. E. Pirani,D. C. Robinson,W. F. Shadwick Book 1979 D. R

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,Bäcklund Maps : General Case,n the first. We proceed as far as possible along the lines laid down in section 3: Let M, N. and N. be C. mainfolds, and let . be a C. map. In the following, it is to be understood that h is a fixed positive integer, while k, l, m, n, q and s are non-negative integers whose ranges are specified in c

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Connections,ed in the language of that theory. Equations (3.15) for example, suggest that a connection is lurking somewhere. In this section we propose two related formulations of Bäcklund maps in terms of connections. In section 7 we employ these formulations to give a geometric interpretation of the “KdV Lie

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,Solutions of the Bäcklund Problem,n now to the main practical problem which is to find Bäcklund maps whose integrability conditions are a given system of partial differential equations. On the face of it, the solution to this problem, which we have called the Bäcklund problem, requires the determination of functions ψ. such that . (

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Introduction,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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Jet Bundles,lications we have in mind are rather different from theirs, but we should mention that the idea of a contact module, introduced in this section, is taken from Johnson’s paper, and the definition of a prolongation imitated from Goldschmidt’s.

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