Cambridge Studies in Advanced Mathematics, Volume 114, Cambridge University Press, Cambridge, 2008

Soliton Equations and Their Algebro-Geometric Solutions. Volume II: (1+1)-Dimensional Discrete Models

Fritz Gesztesy, Helge Holden, Johanna Michor, and Gerald Teschl

The focus of this book is on algebro-geometric solutions of completely integrable, nonlinear, difference-differential equations in (1+1)-dimensions, also known as soliton equations. Explicitly treated integrable models include the Toda, Kac-van Moerbeke, and Ablowitz-Ladik hierarchies. An extensive treatment of the class of algebro-geometric solutions in the stationary as well as time-dependent contexts is provided. The formalism presented includes trace formulas, Dubrovin-type initial value problems, Baker-Akhiezer functions, and theta function representations of all relevant quantities involved. The book uses techniques from the theory of differential equations, spectral analysis, and elements of algebraic geometry (most notably, the theory of compact Riemann surfaces). The presentation is rigorous, detailed, and self-contained with ample background material. Detailed notes for each chapter together with an extensive bibliography enhance the presentation offered in the main text.

MSC2000: Primary 37K15, 37K10; Secondary 39A12, 35Q55
Keywords: Toda hierarchy, Kac-van Moerbeke hierarchy, Ablowitz-Ladik hierarchy, discrete NLS, algebro-geometric solutions.

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Ordering Details
Cover Publisher:Cambridge University Press
Series: Cambridge Studies in Advanced Mathematics
Volume: 114
Publication Year: 2008
Paging: 450 pp; hardcover
List Price: £75
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Table of contents
1. The Toda hierarchy
2. The Kac-van Moerbeke hierarchy
3. The Ablowitz-Ladik hierarchy
Appendix A. Algebraic curves and their theta functions in a nutshell
Appendix B. Hyperelliptic curves of the Toda-type
Appendix C. Asymptotic spectral parameter expansions
Appendix D. Lagrange interpolation
List of symbols
Volume I
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