Product 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.

Product Details

• Amazon Sales Rank: #750447 in Books
• Published on: 2002-06-24
• Original language: English
• Number of items: 1
• Binding: Paperback
• 416 pages

Review
'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