Bäcklund and Darboux Transformations: Geometry and Modern Applications in Soliton Theory (Cambridge Texts in Applied Mathematics, Series Number 30) 1st Edition by C. Rogers (PDF)

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.

User’s Reviews

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

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