Local Jet Bundle Formulation of Bäcklund Transformations. With applications to non-linear evolution equations.

Pirani, F. A. E. / Robinson, D. C. / Shadwick, W. F.

ISBN 10: 9027710368 / ISBN 13: 9789027710369

Published by D. Reidel Publishing Company, Dordrecht, Holland / Boston, U.S.A. / London, England, 1979

About this Item

24 x 16 cm. Paperback. viii, 132 pages. Text in English. Very good condition, see picture. Volume 1 in the series Mathematical Physics Studies, a Supplementary Series to Letters in Mathematical Physics. 250g.

Seller Inventory # 84831

Bibliographic Details

• Title: Local Jet Bundle Formulation of Bäcklund Transformations. With applications to non-linear evolution equations.
• Publisher: D. Reidel Publishing Company, Dordrecht, Holland / Boston, U.S.A. / London, England
• Publication Date: 1979
• Language: English
• ISBN 10: 9027710368
• ISBN 13: 9789027710369
• Binding: Soft cover
• Weight: 250 grams
• Seller catalogs:
  • Wiskunde

About this title

Synopsis

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.