Soliton Equations and Their Algebro-Geometric Solutions: Volume 2, (1+1)-Dimensional Discrete Models

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Fritz Gesztesy (University of Missouri, Columbia) Helge Holden (Norwegian University of Science and Technology, Trondheim)

Soliton Equations and Their Algebro-Geometric Solutions

Volume 2, (1+1)-Dimensional Discrete Models

Fritz Gesztesy (University of Missouri, Columbia), Helge Holden (Norwegian University of Science and Technology, Trondheim), Johanna Michor (Universität Wien, Austria) , Gerald Teschl (Universität Wien, Austria)

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English

Cambridge University Press
04 September 2008

Calculus & mathematical analysis; Analytic topology; Mathematical physics

Series: Cambridge Studies in Advanced Mathematics

As a partner to Volume 1: Dimensional Continuous Models, this monograph provides a self-contained introduction to algebro-geometric solutions of completely integrable, nonlinear, partial differential-difference equations, also known as soliton equations. The systems studied in this volume include the Toda lattice hierarchy, the Kac-van Moerbeke hierarchy, and the Ablowitz-Ladik hierarchy. An extensive treatment of the class of algebro-geometric solutions in the stationary as well as time-dependent contexts is provided. The theory presented includes trace formulas, algebro-geometric initial value problems, Baker-Akhiezer functions, and theta function representations of all relevant quantities involved. The book uses basic techniques from the theory of difference equations and spectral analysis, some elements of algebraic geometry and especially, the theory of compact Riemann surfaces. The presentation is constructive and rigorous, with ample background material provided in various appendices. Detailed notes for each chapter, together with an exhaustive bibliography, enhance understanding of the main results.

By: Fritz Gesztesy (University of Missouri Columbia), Helge Holden (Norwegian University of Science and Technology, Trondheim), Johanna Michor (Universität Wien, Austria), Gerald Teschl (Universität Wien, Austria)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Volume: 114
Dimensions: Height: 234mm, Width: 152mm, Spine: 27mm
Weight: 740g
ISBN: 9780521753081
ISBN 10: 0521753082
Series: Cambridge Studies in Advanced Mathematics
Pages: 448
Publication Date: 04 September 2008
Audience: Professional and scholarly , College/higher education , Undergraduate , Undergraduate , Further / Higher Education
Format: Hardback
Publisher's Status: Active

Acknowledgments; Introduction; 1. The Toda hierarchy; 2. The Kac–van Moerbeke hierarchy; 3. The Ablowitz–Ladik hierarchy; A. Algebraic Curves and Their Theta Functions in a Nutshell; B. Hyperelliptic Curves of the Toda-Type; C. Asymptotic Spectral Parameter Expansions; D. Lagrange Interpolation; List of Symbols; Bibliography; Index; Errata and Addenda for Volume I.

Fritz Gesztesy is Professor of Mathematics at the University of Missouri, Columbia. Helge Holden is Professor of Mathematics at the Norwegian University of Science and Technology. Johanna Michor is a Postdoctoral Fellow in the Faculty of Mathematics at the University of Vienna. Gerald Teschl is Associate Professor of Mathematics at the University of Vienna.

Reviews for Soliton Equations and Their Algebro-Geometric Solutions: Volume 2, (1+1)-Dimensional Discrete Models

Reviews of Volume 1: '... this is a book that I would recommend to any student of mine, for clarity and completeness of exposition ... Any expert as well would enjoy the book and learn something stimulating from the sidenotes that point to alternative developments. We look forward to volumes two and three!' Mathematical Reviews 'The book is very well organized and carefully written. It could be particularly useful for analysts wanting to learn new methods coming from algebraic geometry.' EMS Newsletter Review of Volume 2: 'As with the first part, the book is very well written and carefully organised and it is a pleasure to read it.' EMS Newsletter