Soliton equations and their algebro-geometric solutions. Volume I, (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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| その他の著者: | |
| フォーマット: | Licensed eBooks |
| 言語: | 英語 |
| 出版事項: |
Cambridge, UK ; New York :
Cambridge University Press,
2003.
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| シリーズ: | Cambridge studies in advanced mathematics ;
79. |
| オンライン･アクセス: | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=120684 |
| 要約: | 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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| 物理的記述: | 1 online resource (1 volume) : illustrations |
| 書誌: | Includes bibliographical references (v. 1, pages 469-499) and index. |
| ISBN: | 0511066570 9780511066573 1280417757 9781280417757 0521753074 |