Electronic ISBN:  9781470402303 
Product Code:  MEMO/135/641.E 
79 pp 
List Price:  $47.00 
MAA Member Price:  $42.30 
AMS Member Price:  $28.20 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 135; 1998MSC: Primary 39; 35;
In this work, the authors provide a selfcontained discussion of all realvalued quasiperiodic finitegap solutions of the Toda and Kacvan Moerbeke hierarchies of completely integrable evolution equations. The approach utilizes algebrogeometric methods, factorization techniques for finite difference expressions, as well as Miuratype 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.
 Selfcontained development.
 Novel results for the Kacvan Moerbeke hierarchy and its algebrogeometric solutions.
ReadershipGraduate 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 BakerAkhiezer function

4. Spectral theory for finitegap Jacobi operators

5. Quasiperiodic finitegap solutions of the stationary Toda hierarchy

6. Quasiperiodic finitegap solutions of the Toda hierarchy and the timedependent BakerAkhiezer function

7. The Kacvan Moerbeke hierarchy and its relation to the Toda hierarchy

8. Spectral theory for finitegap Diractype difference operators

9. Quasiperiodic finitegap solutions of the Kacvan Moerbeke hierarchy


Request Review Copy

Get Permissions
 Book Details
 Table of Contents

 Request Review Copy
 Get Permissions
In this work, the authors provide a selfcontained discussion of all realvalued quasiperiodic finitegap solutions of the Toda and Kacvan Moerbeke hierarchies of completely integrable evolution equations. The approach utilizes algebrogeometric methods, factorization techniques for finite difference expressions, as well as Miuratype 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.
 Selfcontained development.
 Novel results for the Kacvan Moerbeke hierarchy and its algebrogeometric 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 BakerAkhiezer function

4. Spectral theory for finitegap Jacobi operators

5. Quasiperiodic finitegap solutions of the stationary Toda hierarchy

6. Quasiperiodic finitegap solutions of the Toda hierarchy and the timedependent BakerAkhiezer function

7. The Kacvan Moerbeke hierarchy and its relation to the Toda hierarchy

8. Spectral theory for finitegap Diractype difference operators

9. Quasiperiodic finitegap solutions of the Kacvan Moerbeke hierarchy