Description: Soliton Equations and their Algebro-Geometric Solutions: Volume 1, (1+1)-Dimensional Continuous Models This book offers a detailed treatment of a class of algebro-geometric solutions and their representations. Fritz Gesztesy (Author), Helge Holden (Author) 9780521753074, Cambridge University Press Hardback, published 5 June 2003 518 pages 22.9 x 15.2 x 3.3 cm, 0.784 kg '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 The focus of this book is on algebro-geometric solutions of completely integrable nonlinear partial differential equations in (1+1)-dimensions, also known as soliton equations. Explicitly treated integrable models include the KdV, AKNS, sine-Gordon, and Camassa-Holm hierarchies as well as the classical massive Thirring system. An extensive treatment of the class of algebro-geometric solutions in the stationary as well as time-dependent contexts is provided. The formalism presented includes trace formulas, Dubrovin-type initial value problems, Baker-Akhiezer functions, and theta function representations of all relevant quantities involved. The book uses techniques from the theory of differential equations, spectral analysis, and elements of algebraic geometry (most notably, the theory of compact Riemann surfaces). The presentation is rigorous, detailed, and self-contained, with ample background material provided in various appendices. Detailed notes for each chapter together with an exhaustive bibliography enhance the presentation offered in the main text. Introduction 1. The KdV hierarchy 2. The sGmKdV hierarchy 3. The AKNS hierarchy 4. The classical massive Thirring system 5. The Camassa–Holm hierarchy Appendix A. Algebraic curves and their theta functions Appendix B. KdV-type curves Appendix C. AKNS-type curves Appendix D. Asymptotic spectral parameter expansions Appendix E. Lagrange interpolation Appendix F. Symmetric functions Appendix G. KdV and AKNS Darboux-type transformations Appendix H. Elliptic functions Appendix I. Herglotz functions Appendix J. Weyl-Titchmarsh theory List of symbols Bibliography Index. Subject Areas: Nonlinear science [PBWR], Geometry [PBM]
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BIC Subject Area 1: Nonlinear science [PBWR]
BIC Subject Area 2: Geometry [PBM]
Number of Pages: 518 Pages
Language: English
Publication Name: Soliton Equations and their Algebro-Geometric Solutions: Volume 1, (1+1)-Dimensional Continuous Models
Publisher: Cambridge University Press
Publication Year: 2003
Subject: Mathematics
Item Height: 229 mm
Item Weight: 784 g
Type: Textbook
Author: Helge Holden, Fritz Gesztesy
Series: Cambridge Studies in Advanced Mathematics
Item Width: 152 mm
Format: Hardcover
