Format:
1 online resource (x, 438 pages)
ISBN:
9780521753081
,
9780511543203
Series Statement:
Cambridge studies in advanced mathematics 114
Content:
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.
Note:
Title from publisher's bibliographic system (viewed on 05 Oct 2015)
Additional Edition:
ISBN 9780521753081
Additional Edition:
Gesztesy, Fritz, 1953 - Soliton equations and their algebro-geometric solutions ; 2: (1 + 1)-Dimensional discrete models Cambridge [u.a.] : Cambridge University Press, 2008 ISBN 9780521753081
Additional Edition:
Erscheint auch als Druck-Ausgabe ISBN 9780521753081
Language:
English
Subjects:
Mathematics
DOI:
10.1017/CBO9780511543203
Author information:
Gesztesy, Fritz 1953-
