Algebro-geometric Quasi-periodic Finite-gap Solutions of the Toda and Kac-van Moerbeke Hierarchies (Memoirs of the American Mathematical Society No. 6

Algebro-geometric Quasi-periodic Finite-gap Solutions of the Toda and Kac-van Moerbeke Hierarchies (Memoirs of the American Mathematical Society No. 6

By: etc. (author), Gerald Teschl (author), W. Bulla (author), Fritz Gesztesy (author), H. Holden (author)Paperback

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Description

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. It features a simple and unified treatment of the topic. It has self-contained development. There are novel results for the Kac-van Moerbeke hierarchy and its algebro-geometric solutions.

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Contents

Introduction The Toda hierarchy, recursion relations, and hyperelliptic curves The stationary Baker-Akhiezer function Spectral theory for finite-gap Jacobi operators Quasi-periodic finite-gap solutions of the stationary Toda hierarchy Quasi-periodic finite-gap solutions of the Toda hierarchy and the time-dependent Baker-Akhiezer function The Kac-van Moerbeke hierarchy and its relation to the Toda hierarchy Spectral theory for finite-gap Dirac-type difference operators Quasi-periodic finite-gap solutions of the Kac-van Moerbeke hierarchy Hyperelliptic curves of the Toda-type and theta functions Periodic Jacobi operators Examples, $g-0,1$ Acknowledgments Bibliography.

Product Details

  • publication date: 15/08/1998
  • ISBN13: 9780821808085
  • Format: Paperback
  • Number Of Pages: 79
  • ID: 9780821808085
  • weight: 198
  • ISBN10: 0821808087

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