Bäcklund and Darboux transformations: geometry and modern applications in soliton theory
This book describes the remarkable connections that exist between the classical differential geometry of surfaces and modern soliton theory. The authors also explore the extensive body of literature from the nineteenth and early twentieth centuries by such eminent geometers as Bianchi, Darboux, Bäck...
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| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2002
|
| Series: | Cambridge texts in applied mathematics
30 |
| Subjects: | |
| Online Access: | BSB01 FHN01 Volltext |
| Summary: | This book describes the remarkable connections that exist between the classical differential geometry of surfaces and modern soliton theory. The authors also explore the extensive body of literature from the nineteenth and early twentieth centuries by such eminent geometers as Bianchi, Darboux, Bäcklund, and Eisenhart on transformations of privileged classes of surfaces which leave key geometric properties unchanged. Prominent amongst these are Bäcklund-Darboux transformations with their remarkable associated nonlinear superposition principles and importance in soliton theory. It is with these transformations and the links they afford between the classical differential geometry of surfaces and the nonlinear equations of soliton theory that the present text is concerned. In this geometric context, solitonic equations arise out of the Gauß-Mainardi-Codazzi equations for various types of surfaces that admit invariance under Bäcklund-Darboux transformations. This text is appropriate for use at a higher undergraduate or graduate level for applied mathematicians or mathematical physics |
| Item Description: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Physical Description: | 1 online resource (xvii, 413 pages) |
| ISBN: | 9780511606359 |
| DOI: | 10.1017/CBO9780511606359 |
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| 520 | |a This book describes the remarkable connections that exist between the classical differential geometry of surfaces and modern soliton theory. The authors also explore the extensive body of literature from the nineteenth and early twentieth centuries by such eminent geometers as Bianchi, Darboux, Bäcklund, and Eisenhart on transformations of privileged classes of surfaces which leave key geometric properties unchanged. Prominent amongst these are Bäcklund-Darboux transformations with their remarkable associated nonlinear superposition principles and importance in soliton theory. It is with these transformations and the links they afford between the classical differential geometry of surfaces and the nonlinear equations of soliton theory that the present text is concerned. In this geometric context, solitonic equations arise out of the Gauß-Mainardi-Codazzi equations for various types of surfaces that admit invariance under Bäcklund-Darboux transformations. This text is appropriate for use at a higher undergraduate or graduate level for applied mathematicians or mathematical physics | ||
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| id | DE-604.BV043940983 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:14Z |
| institution | BVB |
| isbn | 9780511606359 |
| language | English |
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| physical | 1 online resource (xvii, 413 pages) |
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| publishDate | 2002 |
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| publisher | Cambridge University Press |
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| series2 | Cambridge texts in applied mathematics |
| spelling | Rogers, C. Verfasser aut Bäcklund and Darboux transformations geometry and modern applications in soliton theory C. Rogers, W.K. Schief Bäcklund & Darboux Transformations Cambridge Cambridge University Press 2002 1 online resource (xvii, 413 pages) txt rdacontent c rdamedia cr rdacarrier Cambridge texts in applied mathematics 30 Title from publisher's bibliographic system (viewed on 05 Oct 2015) This book describes the remarkable connections that exist between the classical differential geometry of surfaces and modern soliton theory. The authors also explore the extensive body of literature from the nineteenth and early twentieth centuries by such eminent geometers as Bianchi, Darboux, Bäcklund, and Eisenhart on transformations of privileged classes of surfaces which leave key geometric properties unchanged. Prominent amongst these are Bäcklund-Darboux transformations with their remarkable associated nonlinear superposition principles and importance in soliton theory. It is with these transformations and the links they afford between the classical differential geometry of surfaces and the nonlinear equations of soliton theory that the present text is concerned. In this geometric context, solitonic equations arise out of the Gauß-Mainardi-Codazzi equations for various types of surfaces that admit invariance under Bäcklund-Darboux transformations. This text is appropriate for use at a higher undergraduate or graduate level for applied mathematicians or mathematical physics Solitons Bäcklund transformations Darboux transformations Schief, W. K. 1964- Sonstige oth Erscheint auch als Druckausgabe 978-0-521-01288-1 Erscheint auch als Druckausgabe 978-0-521-81331-0 https://doi.org/10.1017/CBO9780511606359 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Rogers, C. Bäcklund and Darboux transformations geometry and modern applications in soliton theory Solitons Bäcklund transformations Darboux transformations |
| title | Bäcklund and Darboux transformations geometry and modern applications in soliton theory |
| title_alt | Bäcklund & Darboux Transformations |
| title_auth | Bäcklund and Darboux transformations geometry and modern applications in soliton theory |
| title_exact_search | Bäcklund and Darboux transformations geometry and modern applications in soliton theory |
| title_full | Bäcklund and Darboux transformations geometry and modern applications in soliton theory C. Rogers, W.K. Schief |
| title_fullStr | Bäcklund and Darboux transformations geometry and modern applications in soliton theory C. Rogers, W.K. Schief |
| title_full_unstemmed | Bäcklund and Darboux transformations geometry and modern applications in soliton theory C. Rogers, W.K. Schief |
| title_short | Bäcklund and Darboux transformations |
| title_sort | backlund and darboux transformations geometry and modern applications in soliton theory |
| title_sub | geometry and modern applications in soliton theory |
| topic | Solitons Bäcklund transformations Darboux transformations |
| topic_facet | Solitons Bäcklund transformations Darboux transformations |
| url | https://doi.org/10.1017/CBO9780511606359 |
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