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Soliton Equations and Their Algebro-Geometric Solutions

Volume 2. (1+1)-Dimensional Discrete Models

$147.00 (C)

Part of Cambridge Studies in Advanced Mathematics

  • Date Published: September 2008
  • availability: Available
  • format: Hardback
  • isbn: 9780521753081

$ 147.00 (C)

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About the Authors
  • As a partner to Volume 1: Dimensional Continuous Models, this book provides a self-contained introduction to solition equations. The systems studied in this volume include the Toda lattice hierarchy, the Kac-van Moerbeke hierarchy, and the Ablowitz-Ladik hierarchy. An extensive treatment of the class of algebro-geometric solutions in the stationary as well as time-dependent contexts is provided. The theory presented includes trace formulas, algebro-geometric initial value problems, Baker-Akhiezer functions, and theta function representations of all relevant quantities involved. The book uses basic techniques from the theory of difference equations and spectral analysis, some elements of algebraic geometry and especially, the theory of compact Riemann surfaces. The presentation is constructive and rigorous, with ample background material provided in various appendices.

    • A detailed treatment of the class of algebro-geometric solutions and their representations in terms of Riemann theta functions
    •  Rigorous and self-contained presentation at graduate level
    •  Four appendices and an exhaustive bibliography provide extensive background material
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    Reviews & endorsements

    "The authors do a superb job at clarity and detail; very subtle features of existence, almost periodicity and reality conditions are also developed. Paraphrasing journalist John Gunther, "tell your audience what you are going to say, say it, then tell them what you said". I called the theory beautiful because it combines algebra and analysis, to provide satisfying, exact solutions to important nonlinear problems that arise in the real world. It does so by giving a geometric explanation of the persistence of symmetry, and allows the modeling of (multi-) solition solutions. This book, in my opinion, does the theory full justice."
    Emma Previato, Mathematical Reviews

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    Product details

    • Date Published: September 2008
    • format: Hardback
    • isbn: 9780521753081
    • length: 448 pages
    • dimensions: 234 x 152 x 27 mm
    • weight: 0.74kg
    • availability: Available
  • Table of Contents

    1. The Toda hierarchy
    2. The Kac–van Moerbeke hierarchy
    3. The Ablowitz–Ladik hierarchy
    A. Algebraic Curves and Their Theta Functions in a Nutshell
    B. Hyperelliptic Curves of the Toda-Type
    C. Asymptotic Spectral Parameter Expansions
    D. Lagrange Interpolation
    List of Symbols
    Errata and Addenda for Volume I.

  • Resources for

    Soliton Equations and Their Algebro-Geometric Solutions

    Fritz Gesztesy, Helge Holden, Johanna Michor, Gerald Teschl

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  • Authors

    Fritz Gesztesy, University of Missouri, Columbia
    Fritz Gesztesy is Professor of Mathematics at the University of Missouri, Columbia.

    Helge Holden, Norwegian University of Science and Technology, Trondheim
    Helge Holden is Professor of Mathematics at the Norwegian University of Science and Technology.

    Johanna Michor, Universität Wien, Austria
    Johanna Michor is a Postdoctoral Fellow in the Faculty of Mathematics at the University of Vienna.

    Gerald Teschl, Universität Wien, Austria
    Gerald Teschl is Associate Professor of Mathematics at the University of Vienna.

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