Local Jet Bundle Formulation of Bäckland Transformations: With Applications to Non-Linear Evolution Equations (Mathematical Physics Studies): 1 - Brossura
Sinossi
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.
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Contenuti
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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Book by Pirani FAE Robinson DC Shadwick WF
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Local Jet Bundle Formulation of Bäckland Transformations: With Applications to Non-Linear Evolution Equations (Mathematical Physics Studies 1)
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D. Reidel Publishing, 1979
ISBN 10: 9027710368
ISBN 13: 9789027710369
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Local Jet Bundle Formulation of Bäcklund Transformations. With Applications to Non-Linear Evolution Equations.
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Hardcover. Condizione: Gut. Dordrecht, Reidel (1979). gr.8°. VIII, 132 p. Pbck. (slightly bumped).- Mathematical Physics Studies, 1.- Few pencil annotations. Codice articolo 85397
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Local Jet Bundle Formulation of Bäckland Transformations
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ISBN 13: 9789027710369
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Taschenbuch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 144 pp. Englisch. Codice articolo 9789027710369
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Local Jet Bundle Formulation of Baeckland Transformations
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Local Jet Bundle Formulation of Backlund Transformations: With Applications to Nonlinear Evolution Equations (Synthese Language Library)
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Local Jet Bundle Formulation of Bäckland Transformations
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Springer, Springer Okt 1979, 1979
ISBN 10: 9027710368
ISBN 13: 9789027710369
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Taschenbuch. Condizione: Neu. This item is printed on demand - Print on Demand Titel. Neuware -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.Springer-Verlag KG, Sachsenplatz 4-6, 1201 Wien 144 pp. Englisch. Codice articolo 9789027710369
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Local Jet Bundle Formulation of Bäckland Transformations : With Applications to Non-Linear Evolution Equations
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Springer Netherlands, Springer Netherlands, 1979
ISBN 10: 9027710368
ISBN 13: 9789027710369
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Taschenbuch. Condizione: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. Codice articolo 9789027710369
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