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Algebro-geometric quasi-periodic finite-gap solutions of the Toda and Kac-van Moerbeke hierarchies

About this Title

W. Bulla, F. Gesztesy, H. Holden and G. Teschl

Publication: Memoirs of the American Mathematical Society
Publication Year: 1998; Volume 135, Number 641
ISBNs: 978-0-8218-0808-5 (print); 978-1-4704-0230-3 (online)
DOI: https://doi.org/10.1090/memo/0641
MathSciNet review: 1432141
MSC: Primary 58F07; Secondary 35Q55, 39A12

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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