| eBook ISBN: | 978-1-4704-0230-3 |
| Product Code: | MEMO/135/641.E |
| List Price: | $47.00 |
| MAA Member Price: | $42.30 |
| AMS Member Price: | $28.20 |
| eBook ISBN: | 978-1-4704-0230-3 |
| Product Code: | MEMO/135/641.E |
| List Price: | $47.00 |
| MAA Member Price: | $42.30 |
| AMS Member Price: | $28.20 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 135; 1998; 79 ppMSC: 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.
ReadershipGraduate students, research mathematicians and theoretical physicists working in completely integrable systems.
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Table of Contents
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Chapters
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1. Introduction
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2. The Toda hierarchy, recursion relations, and hyperelliptic curves
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3. The stationary Baker-Akhiezer function
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4. Spectral theory for finite-gap Jacobi operators
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5. Quasi-periodic finite-gap solutions of the stationary Toda hierarchy
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6. Quasi-periodic finite-gap solutions of the Toda hierarchy and the time-dependent Baker-Akhiezer function
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7. The Kac-van Moerbeke hierarchy and its relation to the Toda hierarchy
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8. Spectral theory for finite-gap Dirac-type difference operators
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9. Quasi-periodic finite-gap solutions of the Kac-van Moerbeke hierarchy
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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.
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
