Bäcklund and Darboux Transformations: Geometry and Modern Applications in Soliton Theory (Cambridge Texts in Applied Mathematics, Series Number 30) - Softcover

Rogers, C.; Schief, W. K.

Softcover

ISBN 10: 0521012880 ISBN 13: 9780521012881

Publisher: 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.

About this title

Book Description

This book explores the deep and fascinating connections that exist between a ubiquitous class of physically important waves known as solitons and the theory of transformations of a privileged class of surfaces as they were studied by eminent geometers of the nineteenth century. Thus, nonlinear equations governing soliton propagation and also mathematical descriptions of their remarkable interaction properties are shown to arise naturally out of the classical differential geometry of surfaces and what are termed Bäcklund-Darboux transformations.This text, the first of its kind, is written in a straightforward manner and is punctuated by exercises to test the understanding of the reader. It is suitable for use in higher undergraduate or graduate level courses directed at applied mathematicians or mathematical physics.

Review

"The book can serve as a very good introduction not only for students and young researchers but also for qualified scientists who would like to study nonlinear problems in connection with geometry of submanifolds. Work done in the last few years has proved that interactions between soliton theory and differential geometry are very profitable to both fields." Mathematical Reviews

Edition details

• Publisher: Cambridge University Press
• Publication date: 2002
• Language: English
• ISBN 10: 0521012880
• ISBN 13: 9780521012881
• Binding: Paperback
• Edition number: 1
• Number of pages: 432