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, Backlund, and Eisenhart on transformations of privileged classes of surfaces which leave key geometric properties unchanged. Prominent amongst these are Backlund-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 Backlund-Darboux transformations. This text is appropriate for use at a higher undergraduate or graduate level for applied mathematicians or mathematical physics.

This book explores deep and fascinating connections between a ubiquitous class of physically important waves known as solitons.
Reviews
'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



Book Information
ISBN 9780521012881
Author C. Rogers
Format Paperback
Page Count 432
Imprint Cambridge University Press
Publisher Cambridge University Press
Weight(grams) 596g
Dimensions(mm) 228mm * 153mm * 23mm