Soliton equations and their algebro-geometric solutions. Volume 2, (1 + 1)-dimensional discrete models / Fritz Gesztesy [and three others].

Format:

Book

Author/Creator:

Gesztesy, Fritz, 1953- author.

Series:

Cambridge studies in advanced mathematics ; 114.

Cambridge studies in advanced mathematics ; 114

Language:

English

Subjects (All):

Differential equations, Nonlinear--Numerical solutions.

Differential equations, Nonlinear.

Solitons.

Physical Description:

1 online resource (x, 438 pages) : digital, PDF file(s).

Edition:

1st ed.

Other Title:

Soliton Equations & Their Algebro-Geometric Solutions

Place of Publication:

Cambridge : Cambridge University Press, 2008.

Language Note:

English

Summary:

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.

Contents:

Cover; Half-title; Series-title; Title; Copyright; Contents; Acknowledgments; Introduction; 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 and Nonlinear Recursion Relations; Appendix D: Lagrange Interpolation; List of Symbols; Bibliography; Index; Errata and Addenda for Volume

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references and index.

ISBN:

1-107-19344-3

1-281-79136-9

9786611791360

0-511-42946-0

0-511-42827-8

0-511-42984-3

0-511-42766-2

0-511-54320-4

0-511-42898-7

OCLC:

437222483