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 certa… Meer...
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. Books > Physics eBook, Springer Shop<
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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 certa… Meer...
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. Books > Physics eBook, Springer Shop<
- new in stock. Verzendingskosten:zzgl. Versandkosten., exclusief verzendingskosten
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Gedetalleerde informatie over het boek. - Local Jet Bundle Formulation of Backland Transformations : With Applications to Non-Linear Evolution Equations
Boek bevindt zich in het datenbestand sinds 2017-05-22T23:40:49+02:00 (Amsterdam) Detailpagina laatst gewijzigd op 2021-02-07T19:15:49+01:00 (Amsterdam) ISBN/EAN: 9789400995116
ISBN - alternatieve schrijfwijzen: 978-94-009-9511-6 alternatieve schrijfwijzen en verwante zoekwoorden: Auteur van het boek: robinson Titel van het boek: formulation
Gegevens van de uitgever
Auteur: F.A.E. Pirani; D.C. Robinson; W.F. Shadwick Titel: Mathematical Physics Studies; Local Jet Bundle Formulation of Bäckland Transformations - With Applications to Non-Linear Evolution Equations Uitgeverij: Springer; Springer Netherland 140 Bladzijden Verschijningsjaar: 2012-12-06 Dordrecht; NL Taal: Engels 53,49 € (DE) 55,00 € (AT) 59,00 CHF (CH) Available 140 p.
EA; E107; eBook; Nonbooks, PBS / Physik, Astronomie/Theoretische Physik; Mathematische Physik; Verstehen; evolution; solution; C; Theoretical, Mathematical and Computational Physics; Physics and Astronomy; BC
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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