SOLITON EQUATIONS AND THEIR ALGEBRO-GEOMETRIC SOLUTIONS - VOL. 2

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Sinopse

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. Presentation with ample background material provided in various appendices. Detailed notes for each chapter, together with an exhaustive bibliography, enhance understanding of the main results. Contents: 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.

Ficha técnica

Código de barras:
9780521753081
Dimensões:
2.00cm x 16.00cm x 23.00cm
Edição:
1ª EDIÇÃO - 2008
Editora:
CAMBRIDGE UNIVERSITY PRESS
ISBN:
0521753082
ISBN13:
9780521753081
Número de páginas:
448
Peso:
500 gramas
Ano de publicação:
2008
Capa dura:
Sim