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Algebro-Geometric Quasi-Periodic Finite-Gap Solutions of the Toda and Kac-van Moerbeke Hierarchies
 
W. Bulla Graz Technical University, Austria
F. Gesztesy University of Missouri, Columbia
H. Holden Norwegian University of Science & Technology, Trondheim
G. Teschl Institut für Reine und Angewandte Mathematik, Aachen, Germany
Front Cover for Algebro-Geometric Quasi-Periodic Finite-Gap Solutions of the Toda and Kac-van Moerbeke Hierarchies
Available Formats:
Electronic ISBN: 978-1-4704-0230-3
Product Code: MEMO/135/641.E
79 pp 
List Price: $47.00
MAA Member Price: $42.30
AMS Member Price: $28.20
Front Cover for Algebro-Geometric Quasi-Periodic Finite-Gap Solutions of the Toda and Kac-van Moerbeke Hierarchies
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Algebro-Geometric Quasi-Periodic Finite-Gap Solutions of the Toda and Kac-van Moerbeke Hierarchies
W. Bulla Graz Technical University, Austria
F. Gesztesy University of Missouri, Columbia
H. Holden Norwegian University of Science & Technology, Trondheim
G. Teschl Institut für Reine und Angewandte Mathematik, Aachen, Germany
Available Formats:
Electronic ISBN:  978-1-4704-0230-3
Product Code:  MEMO/135/641.E
79 pp 
List Price: $47.00
MAA Member Price: $42.30
AMS Member Price: $28.20
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 1351998
    MSC: Primary 39; 35;



    In this work, the authors provide a self-contained discussion of all real-valued quasi-periodic finite-gap solutions of the Toda and Kac-van Moerbeke hierarchies of completely integrable evolution equations. The approach utilizes algebro-geometric methods, factorization techniques for finite difference expressions, as well as Miura-type transformations. Detailed spectral theoretic properties of Lax pairs and theta function representations of the solutions are derived.

    Features:

    • Simple and unified treatment of the topic.
    • Self-contained development.
    • Novel results for the Kac-van Moerbeke hierarchy and its algebro-geometric solutions.

    Readership

    Graduate students, research mathematicians and theoretical physicists working in completely integrable systems.

  • Table of Contents
     
     
    • Chapters
    • 1. Introduction
    • 2. The Toda hierarchy, recursion relations, and hyperelliptic curves
    • 3. The stationary Baker-Akhiezer function
    • 4. Spectral theory for finite-gap Jacobi operators
    • 5. Quasi-periodic finite-gap solutions of the stationary Toda hierarchy
    • 6. Quasi-periodic finite-gap solutions of the Toda hierarchy and the time-dependent Baker-Akhiezer function
    • 7. The Kac-van Moerbeke hierarchy and its relation to the Toda hierarchy
    • 8. Spectral theory for finite-gap Dirac-type difference operators
    • 9. Quasi-periodic finite-gap solutions of the Kac-van Moerbeke hierarchy
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Volume: 1351998
MSC: Primary 39; 35;



In this work, the authors provide a self-contained discussion of all real-valued quasi-periodic finite-gap solutions of the Toda and Kac-van Moerbeke hierarchies of completely integrable evolution equations. The approach utilizes algebro-geometric methods, factorization techniques for finite difference expressions, as well as Miura-type transformations. Detailed spectral theoretic properties of Lax pairs and theta function representations of the solutions are derived.

Features:

  • Simple and unified treatment of the topic.
  • Self-contained development.
  • Novel results for the Kac-van Moerbeke hierarchy and its algebro-geometric solutions.

Readership

Graduate students, research mathematicians and theoretical physicists working in completely integrable systems.

  • Chapters
  • 1. Introduction
  • 2. The Toda hierarchy, recursion relations, and hyperelliptic curves
  • 3. The stationary Baker-Akhiezer function
  • 4. Spectral theory for finite-gap Jacobi operators
  • 5. Quasi-periodic finite-gap solutions of the stationary Toda hierarchy
  • 6. Quasi-periodic finite-gap solutions of the Toda hierarchy and the time-dependent Baker-Akhiezer function
  • 7. The Kac-van Moerbeke hierarchy and its relation to the Toda hierarchy
  • 8. Spectral theory for finite-gap Dirac-type difference operators
  • 9. Quasi-periodic finite-gap solutions of the Kac-van Moerbeke hierarchy
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