Local Jet Bundle Formulation of Bäckland Transformations : With Applications to Non-Linear Evolution Equations

The aim of this paper is to show that the theory of jet bundles supplies the appropriate setting for the study of Backlund trans­ formations. These transformations are used to solve certain partial differential equations, particularly non-linear evolution equations. Of course jets have been employed...

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Main Authors: Pirani, F.A.E., Robinson, D.C. (Author), Shadwick, W.F. (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Dordrecht Springer Netherlands 1979, 1979
Edition:1st ed. 1979
Series:Mathematical Physics Studies
Subjects:
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
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100 1 |a Pirani, F.A.E. 
245 0 0 |a Local Jet Bundle Formulation of Bäckland Transformations  |h Elektronische Ressource  |b With Applications to Non-Linear Evolution Equations  |c by F.A.E. Pirani, D.C. Robinson, W.F. Shadwick 
250 |a 1st ed. 1979 
260 |a Dordrecht  |b Springer Netherlands  |c 1979, 1979 
300 |a 140 p  |b online resource 
505 0 |a Section 1. Introduction -- Section 2. Jet Bundles -- Section 3. Bäcklund Maps: Simplest Case -- Section 4. Bäcklund Maps: General Case -- Section 5. Connections -- Section 6. One Parameter Families of Bäcklund Maps -- Section 7. Solutions of the Bäcklund Problem -- References 
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653 |a Theoretical, Mathematical and Computational Physics 
700 1 |a Robinson, D.C.  |e [author] 
700 1 |a Shadwick, W.F.  |e [author] 
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520 |a The aim of this paper is to show that the theory of jet bundles supplies the appropriate setting for the study of Backlund trans­ formations. 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 dis­ covery of remarkable properties of some such equations, for example the existence of soliton solutions and of infinite se­ quences of conservation laws. Among the techniques devised to deal with these equations are the inverse scattering method and the Backlund transformation. In our opinion the jet bundle formulation offers a unifying geometrical framework for under­ standing 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. The relevance of the theory of jet bundles lS that it legitimates the practice of regarding the partial derivatives of field variables as independent quantities. Since Backlund trans­ formations require from the outset manipulation of these partial derivatives, and repeated shifts of point of view about which variables are dependent on which, this geometrical setting clari­ fies and simplifies the concepts involved, and offers the prospect of bringing coherence to a variety of disparate results