Soliton equations and their algebro-geometric solutions: Volume 1 (1 + 1)-dimensional continuous models
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 classi...
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| Format: | E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2003
|
| Schriftenreihe: | Cambridge studies in advanced mathematics
79 |
| Links: | https://doi.org/10.1017/CBO9780511546723 |
| Zusammenfassung: | 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. |
| Umfang: | 1 Online-Ressource (xii, 505 Seiten) |
| ISBN: | 9780511546723 |
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| 520 | |a 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. | ||
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| spelling | Gesztesy, Fritz 1953- Soliton equations and their algebro-geometric solutions Volume 1 (1 + 1)-dimensional continuous models Fritz Gesztesy, Helge Holden Soliton Equations & their Algebro-Geometric Solutions Cambridge Cambridge University Press 2003 1 Online-Ressource (xii, 505 Seiten) txt c cr Cambridge studies in advanced mathematics 79 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. Holden, Helge Erscheint auch als Druck-Ausgabe 9780521753074 |
| spellingShingle | Gesztesy, Fritz 1953- Soliton equations and their algebro-geometric solutions |
| title | Soliton equations and their algebro-geometric solutions |
| title_alt | Soliton Equations & their Algebro-Geometric Solutions |
| title_auth | Soliton equations and their algebro-geometric solutions |
| title_exact_search | Soliton equations and their algebro-geometric solutions |
| title_full | Soliton equations and their algebro-geometric solutions Volume 1 (1 + 1)-dimensional continuous models Fritz Gesztesy, Helge Holden |
| title_fullStr | Soliton equations and their algebro-geometric solutions Volume 1 (1 + 1)-dimensional continuous models Fritz Gesztesy, Helge Holden |
| title_full_unstemmed | Soliton equations and their algebro-geometric solutions Volume 1 (1 + 1)-dimensional continuous models Fritz Gesztesy, Helge Holden |
| title_short | Soliton equations and their algebro-geometric solutions |
| title_sort | soliton equations and their algebro geometric solutions 1 1 dimensional continuous models |
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