Soliton equations and their algebro-geometric solutions: Volume 2 (1 + 1)-dimensional discrete models
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 th...
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| Main Author: | |
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| Format: | eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2008
|
| Series: | Cambridge studies in advanced mathematics
114 |
| Links: | https://doi.org/10.1017/CBO9780511543203 |
| 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. |
| Physical Description: | 1 Online-Ressource (x, 438 Seiten) |
| ISBN: | 9780511543203 |
Staff View
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| spelling | Gesztesy, Fritz 1953- Soliton equations and their algebro-geometric solutions Volume 2 (1 + 1)-dimensional discrete models Fritz Gesztesy [and three others] Soliton Equations & Their Algebro-Geometric Solutions Cambridge Cambridge University Press 2008 1 Online-Ressource (x, 438 Seiten) txt c cr Cambridge studies in advanced mathematics 114 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. Erscheint auch als Druck-Ausgabe 9780521753081 |
| 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 2 (1 + 1)-dimensional discrete models Fritz Gesztesy [and three others] |
| title_fullStr | Soliton equations and their algebro-geometric solutions Volume 2 (1 + 1)-dimensional discrete models Fritz Gesztesy [and three others] |
| title_full_unstemmed | Soliton equations and their algebro-geometric solutions Volume 2 (1 + 1)-dimensional discrete models Fritz Gesztesy [and three others] |
| title_short | Soliton equations and their algebro-geometric solutions |
| title_sort | soliton equations and their algebro geometric solutions 1 1 dimensional discrete models |
| work_keys_str_mv | AT gesztesyfritz solitonequationsandtheiralgebrogeometricsolutionsvolume2 AT gesztesyfritz solitonequationstheiralgebrogeometricsolutions |