Bäcklund and Darboux transformations : geometry and modern applications in soliton theory / C. Rogers, W.K. Schief.

Format:

Book

Author/Creator:

Rogers, C., author.

Schief, W. K. (Wolfgang Karl), 1964- author.

Series:

Cambridge texts in applied mathematics ; 30.

Cambridge texts in applied mathematics ; 30

Language:

English

Subjects (All):

Solitons.

Bäcklund transformations.

Darboux transformations.

Physical Description:

1 online resource (xvii, 413 pages) : digital, PDF file(s).

Edition:

1st ed.

Other Title:

Bäcklund & Darboux Transformations

Place of Publication:

Cambridge : Cambridge University Press, 2002.

Language Note:

English

Summary:

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.

Contents:

Intro

Contents

Preface

Acknowledgements

General Introduction and Outline

Appendix A The su(2)-so(3) Isomorphism

Appendix B CC-Ideals

Appendix C Biographies

Bibliography and Author Index

Subject Index.

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references and index.

ISBN:

0-511-15790-8

0-511-60635-4

0-511-02054-6

OCLC:

847049388