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  • Cited by 429
Publisher:
Cambridge University Press
Online publication date:
March 2010
Print publication year:
2002
Online ISBN:
9780511606359

Book description

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.

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'It is an excellent book for graduate students and young researchers … very useful for scientists in this field.'

Source: 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.'

Source: Bulletin of the Belgian Mathematical Society

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Contents

Bibliography and Author Index
Bibliography and Author Index
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