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Soliton Equations and their Algebro-Geometric Solutions: Volume 1, (1+1)-Dimensional Continuous Models (Cambridge Studies in Advanced Mathe
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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).
- Sales Rank: #4247266 in Books
- Brand: Brand: Cambridge University Press
- Published on: 2003-06-23
- Original language: English
- Number of items: 1
- Dimensions: 8.98" h x 1.26" w x 5.98" l, 1.25 pounds
- Binding: Hardcover
- 518 pages
- Used Book in Good Condition
Review
'... 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 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
About the Author
Fritz Gesztesy is Professor of Mathematics at the University of Missouri, Columbia.
Helge Holden is Professor of Mathematics at the Norwegian University of Science and Technology.
Johanna Michor is a Postdoctoral Fellow in the Faculty of Mathematics at the University of Vienna.
Gerald Teschl is Associate Professor of Mathematics at the University of Vienna.
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