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Look Inside Bäcklund and Darboux Transformations

Bäcklund and Darboux Transformations
Geometry and Modern Applications in Soliton Theory

$180.00 (P)

Part of Cambridge Texts in Applied Mathematics

  • Authors:
  • C. Rogers, University of New South Wales, Sydney
  • W. K. Schief, University of New South Wales, Sydney
  • Date Published: June 2002
  • availability: Available
  • format: Hardback
  • isbn: 9780521813310

$ 180.00 (P)

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About the Authors
  • 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.

    • One of the first books to treat the geometry of soliton theory at graduate textbook level
    • No prior knowledge of soliton theory required
    • Straightforward account punctuated by exercises to test the understanding of the reader
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    Reviews & endorsements

    "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

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    Product details

    • Date Published: June 2002
    • format: Hardback
    • isbn: 9780521813310
    • length: 432 pages
    • dimensions: 229 x 152 x 29 mm
    • weight: 0.8kg
    • contains: 48 b/w illus. 76 exercises
    • availability: Available
  • Table of Contents

    General introduction and outline
    1. Pseudospherical surfaces and the classical Bäcklund transformation: the Bianchi system
    2. The motion of curves and surfaces. soliton connections
    3. Tzitzeica surfaces: conjugate nets and the Toda Lattice scheme
    4. Hasimoto Surfaces and the Nonlinear Schrödinger Equation: Geometry and associated soliton equations
    5. Isothermic surfaces: the Calapso and Zoomeron equations
    6. General aspects of soliton surfaces: role of gauge and reciprocal transfomations
    7. Bäcklund transformation and Darboux matrix connections
    8. Bianchi and Ernst systems: Bäcklund transformations and permutability theorems
    9. Projective-minimal and isothermal-asymptotic surfaces
    A. The su(2)-so(3) isomorphism
    B. CC-ideals
    C. Biographies

  • Authors

    C. Rogers, University of New South Wales, Sydney

    W. K. Schief, University of New South Wales, Sydney

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