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Bäcklund and Darboux Transformations: Geometry and Modern Applications in Soliton Theory - Couverture rigide

Rogers, C.; Schief, W. K.

 
9780521813310: Bäcklund and Darboux Transformations: Geometry and Modern Applications in Soliton Theory
Couverture rigide
ISBN 10 : 052181331X ISBN 13 : 9780521813310
Editeur : Cambridge University Press, 2002

Synopsis

This book describes the remarkable connections that exist between the classical differential geometry of surfaces and modern soliton theory. The authors also explore the extensive body of literature from the nineteenth and early twentieth centuries by such eminent geometers as Bianchi, Darboux, Bäcklund, and Eisenhart on transformations of privileged classes of surfaces which leave key geometric properties unchanged. Prominent amongst these are Bäcklund-Darboux transformations with their remarkable associated nonlinear superposition principles and importance in soliton theory. It is with these transformations and the links they afford between the classical differential geometry of surfaces and the nonlinear equations of soliton theory that the present text is concerned. In this geometric context, solitonic equations arise out of the Gauß-Mainardi-Codazzi equations for various types of surfaces that admit invariance under Bäcklund-Darboux transformations. This text is appropriate for use at a higher undergraduate or graduate level for applied mathematicians or mathematical physics.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Présentation de l'éditeur

This book describes the remarkable connections that exist between the classical differential geometry of surfaces and modern soliton theory. The authors also explore the extensive body of literature from the nineteenth and early twentieth centuries by such eminent geometers as Bianchi, Darboux, Bäcklund, and Eisenhart on transformations of privileged classes of surfaces which leave key geometric properties unchanged. Prominent amongst these are Bäcklund-Darboux transformations with their remarkable associated nonlinear superposition principles and importance in soliton theory. It is with these transformations and the links they afford between the classical differential geometry of surfaces and the nonlinear equations of soliton theory that the present text is concerned. In this geometric context, solitonic equations arise out of the Gauß-Mainardi-Codazzi equations for various types of surfaces that admit invariance under Bäcklund-Darboux transformations. This text is appropriate for use at a higher undergraduate or graduate level for applied mathematicians or mathematical physics.

Revue de presse

'It is an excellent book for graduate students and young researchers ... very useful for scientists in this field.' Nieuw Archief voor Wiskunde

'The book certainly is a recommendable book for everyone who is interested in these transformations as well as in the related geometry and modern applications.' Bulletin of the Belgian Mathematical Society

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
Cambridge University Press
Date d'édition
2002
Langue
anglais
ISBN 10 
052181331X
ISBN 13 
9780521813310
Reliure
Relié
Nombre de pages
432
Coordonnées du fabricant
Cambridge University Press
https://www.cambridge.org/

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