Soliton Equations and Their Algebro-Geometric Solutions: Volume 2, (1+1)-Dimensional Discrete Models
Fritz Gesztesy · Helge Holden · Johanna Michor · Gerald Teschl
Sep 2008 · Cambridge Studies in Advanced Mathematics Book 114 · Cambridge University Press
Ebook
438
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About this ebook
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.
About the author
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.
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