Soliton Equations and their Algebro-Geometric Solutions
Volume 1. (1+1)-Dimensional Continuous Models
$125.00 ( ) USD
- Fritz Gesztesy, University of Missouri, Columbia
- Helge Holden, Norwegian University of Science and Technology, Trondheim
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This book is about 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 and 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).Read more
- Algebro-geometric solutions of completely integrable nonlinear partial differential equations in (1+1)-dimensions
- Rigorous, detailed, and self-contained presentation
- Presentation based on mathematical analysis with emphasis on spectral theoretic methods
Reviews & endorsements
'… this is a book that I would recommend to any student of mine, for clarity and completeness of exposition … Any expert as well would enjoy the book and learn something stimulating from the sidenotes that point to alternative developments. We look forward to volumes two and three!' Mathematical ReviewsSee more reviews
'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
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- Date Published: December 2004
- format: Adobe eBook Reader
- isbn: 9780511060267
- availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
Table of Contents
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
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