Memoirs of the American Mathematical Society 1998; 79 pp; softcover Volume: 135 ISBN10: 0821808087 ISBN13: 9780821808085 List Price: US$44 Individual Members: US$26.40 Institutional Members: US$35.20 Order Code: MEMO/135/641
 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.
Readership Graduate students, research mathematicians and theoretical physicists working in completely integrable systems. Table of Contents  Introduction
 The Toda hierarchy, recursion relations, and hyperelliptic curves
 The stationary BakerAkhiezer function
 Spectral theory for finitegap Jacobi operators
 Quasiperiodic finitegap solutions of the stationary Toda hierarchy
 Quasiperiodic finitegap solutions of the Toda hierarchy and the timedependent BakerAkhiezer function
 The Kacvan Moerbeke hierarchy and its relation to the Toda hierarchy
 Spectral theory for finitegap Diractype difference operators
 Quasiperiodic finitegap solutions of the Kacvan Moerbeke hierarchy
 Hyperelliptic curves of the Todatype and theta functions
 Periodic Jacobi operators
 Examples, \(g0,1\)
 Acknowledgments
 Bibliography
