02993nmm a2200301 u 4500001001200000003002700012005001700039007002400056008004100080020001800121100001900139245018800158250001700346260004800363300002700411505028500438653002500723653005600748700002900804700002900833710003400862041001900896989003800915490003300953856007200986082001001058520162301068EB000714385EBX0100000000000000056746700000000000000.0cr|||||||||||||||||||||140122 ||| eng a97894009951161 aPirani, F.A.E.00aLocal Jet Bundle Formulation of Bäckland TransformationshElektronische RessourcebWith Applications to Non-Linear Evolution Equationscby F.A.E. Pirani, D.C. Robinson, W.F. Shadwick a1st ed. 1979 aDordrechtbSpringer Netherlandsc1979, 1979 a140 pbonline resource0 aSection 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 aMathematical physics aTheoretical, Mathematical and Computational Physics1 aRobinson, D.C.e[author]1 aShadwick, W.F.e[author]2 aSpringerLink (Online service)07aeng2ISO 639-2 bSBAaSpringer Book Archives -20040 aMathematical Physics Studies uhttps://doi.org/10.1007/978-94-009-9511-6?nosfx=yxVerlag3Volltext0 a530.1 aThe 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