Skip to content
Register Sign in Wishlist

Soliton Equations and Their Algebro-Geometric Solutions

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

Part of Cambridge Studies in Advanced Mathematics

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

Hardback

Add to wishlist

Other available formats:
eBook


Looking for an inspection copy?

This title is not currently available on inspection

Description
Product filter button
Description
Contents
Resources
Courses
About the Authors
  • As a partner to Volume 1: Dimensional Continuous Models, this monograph provides a self-contained introduction to algebro-geometric solutions of completely integrable, nonlinear, partial differential-difference equations, also known as soliton 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. Detailed notes for each chapter, together with an exhaustive bibliography, enhance understanding of the main results.

    • 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
    Read more

    Reviews & endorsements

    Reviews of Volume 1: '… this is a book that I would recommend to any student of mine, for clarity and completeness of exposition … Any expert as well would enjoy the book and learn something stimulating from the sidenotes that point to alternative developments. We look forward to volumes two and three!' Mathematical Reviews

    'The book is very well organized and carefully written. It could be particularly useful for analysts wanting to learn new methods coming from algebraic geometry.' EMS Newsletter

    Review of Volume 2: 'As with the first part, the book is very well written and carefully organised and it is a pleasure to read it.' EMS Newsletter

    See more reviews

    Customer reviews

    Not yet reviewed

    Be the first to review

    Review was not posted due to profanity

    ×

    , create a review

    (If you're not , sign out)

    Please enter the right captcha value
    Please enter a star rating.
    Your review must be a minimum of 12 words.

    How do you rate this item?

    ×

    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

    Acknowledgments
    Introduction
    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
    Bibliography
    Index
    Errata and Addenda for Volume I.

  • Resources for

    Soliton Equations and Their Algebro-Geometric Solutions

    Fritz Gesztesy, Helge Holden, Johanna Michor, Gerald Teschl

    General Resources

    Find resources associated with this title

    Type Name Unlocked * Format Size

    Showing of

    Back to top

    This title is supported by one or more locked resources. Access to locked resources is granted exclusively by Cambridge University Press to lecturers whose faculty status has been verified. To gain access to locked resources, lecturers should sign in to or register for a Cambridge user account.

    Please use locked resources responsibly and exercise your professional discretion when choosing how you share these materials with your students. Other lecturers may wish to use locked resources for assessment purposes and their usefulness is undermined when the source files (for example, solution manuals or test banks) are shared online or via social networks.

    Supplementary resources are subject to copyright. Lecturers are permitted to view, print or download these resources for use in their teaching, but may not change them or use them for commercial gain.

    If you are having problems accessing these resources please contact lecturers@cambridge.org.

  • 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.

Sorry, this resource is locked

Please register or sign in to request access. If you are having problems accessing these resources please email lecturers@cambridge.org

Register Sign in
Please note that this file is password protected. You will be asked to input your password on the next screen.

» Proceed

You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner www.ebooks.com. Please see the permission section of the www.ebooks.com catalogue page for details of the print & copy limits on our eBooks.

Continue ×

Continue ×

Continue ×
warning icon

Turn stock notifications on?

You must be signed in to your Cambridge account to turn product stock notifications on or off.

Sign in Create a Cambridge account arrow icon
×

Find content that relates to you

Join us online

This site uses cookies to improve your experience. Read more Close

Are you sure you want to delete your account?

This cannot be undone.

Cancel

Thank you for your feedback which will help us improve our service.

If you requested a response, we will make sure to get back to you shortly.

×
Please fill in the required fields in your feedback submission.
×