The direct method in soliton theory:
The bilinear, or Hirota's direct, method was invented in the early 1970s as an elementary means of constructing soliton solutions that avoided the use of the heavy machinery of the inverse scattering transform and was successfully used to construct the multisoliton solutions of many new equatio...
Gespeichert in:
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| Weitere Verfasser: | , , |
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2004
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| Schriftenreihe: | Cambridge tracts in mathematics
155 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 UBR01 URL des Erstveröffentlichers |
| Zusammenfassung: | The bilinear, or Hirota's direct, method was invented in the early 1970s as an elementary means of constructing soliton solutions that avoided the use of the heavy machinery of the inverse scattering transform and was successfully used to construct the multisoliton solutions of many new equations. In the 1980s the deeper significance of the tools used in this method - Hirota derivatives and the bilinear form - came to be understood as a key ingredient in Sato's theory and the connections with affine Lie algebras. The main part of this book concerns the more modern version of the method in which solutions are expressed in the form of determinants and pfaffians. While maintaining the original philosophy of using relatively simple mathematics, it has, nevertheless, been influenced by the deeper understanding that came out of the work of the Kyoto school. The book will be essential for all those working in soliton theory |
| Beschreibung: | 1 Online-Ressource (xi, 200 Seiten) |
| ISBN: | 9780511543043 |
| DOI: | 10.1017/CBO9780511543043 |
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| 240 | 1 | 0 | |a Chokusetsuhō ni yoru soriton no sūri |
| 245 | 1 | 0 | |a The direct method in soliton theory |c Ryogo Hirota ; translated from Japanese and edited by Atsushi Nagai, Jon Nimmo, and Claire Gilson |
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| 505 | 8 | |a 1. Bilinearization of soliton equations -- 2. Determinants and pfaffians -- 3. Structure of soliton equations -- 4. Backlund transformations -- Afterword -- References -- Index | |
| 520 | |a The bilinear, or Hirota's direct, method was invented in the early 1970s as an elementary means of constructing soliton solutions that avoided the use of the heavy machinery of the inverse scattering transform and was successfully used to construct the multisoliton solutions of many new equations. In the 1980s the deeper significance of the tools used in this method - Hirota derivatives and the bilinear form - came to be understood as a key ingredient in Sato's theory and the connections with affine Lie algebras. The main part of this book concerns the more modern version of the method in which solutions are expressed in the form of determinants and pfaffians. While maintaining the original philosophy of using relatively simple mathematics, it has, nevertheless, been influenced by the deeper understanding that came out of the work of the Kyoto school. The book will be essential for all those working in soliton theory | ||
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Datensatz im Suchindex
| _version_ | 1804176883523256320 |
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| any_adam_object | |
| author | Hirota, Ryogo 1932- |
| author2 | Nagai, Atsushi Nagai, Atsushi Nimmo, J. J. C. Nimmo, J. J. C. Gilson, Claire Gilson, Claire |
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| author_GND | (DE-588)173706363 |
| author_facet | Hirota, Ryogo 1932- Nagai, Atsushi Nagai, Atsushi Nimmo, J. J. C. Nimmo, J. J. C. Gilson, Claire Gilson, Claire |
| author_role | aut |
| author_sort | Hirota, Ryogo 1932- |
| author_variant | r h rh |
| building | Verbundindex |
| bvnumber | BV043941579 |
| classification_rvk | SK 950 |
| collection | ZDB-20-CBO |
| contents | 1. Bilinearization of soliton equations -- 2. Determinants and pfaffians -- 3. Structure of soliton equations -- 4. Backlund transformations -- Afterword -- References -- Index |
| ctrlnum | (ZDB-20-CBO)CR9780511543043 (OCoLC)699176383 (DE-599)BVBBV043941579 |
| dewey-full | 530.12/4 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.12/4 |
| dewey-search | 530.12/4 |
| dewey-sort | 3530.12 14 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| doi_str_mv | 10.1017/CBO9780511543043 |
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| id | DE-604.BV043941579 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:16Z |
| institution | BVB |
| isbn | 9780511543043 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029350549 |
| oclc_num | 699176383 |
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| physical | 1 Online-Ressource (xi, 200 Seiten) |
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| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Cambridge University Press |
| record_format | marc |
| series2 | Cambridge tracts in mathematics |
| spelling | Hirota, Ryogo 1932- Verfasser (DE-588)173706363 aut Chokusetsuhō ni yoru soriton no sūri The direct method in soliton theory Ryogo Hirota ; translated from Japanese and edited by Atsushi Nagai, Jon Nimmo, and Claire Gilson Cambridge Cambridge University Press 2004 1 Online-Ressource (xi, 200 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge tracts in mathematics 155 1. Bilinearization of soliton equations -- 2. Determinants and pfaffians -- 3. Structure of soliton equations -- 4. Backlund transformations -- Afterword -- References -- Index The bilinear, or Hirota's direct, method was invented in the early 1970s as an elementary means of constructing soliton solutions that avoided the use of the heavy machinery of the inverse scattering transform and was successfully used to construct the multisoliton solutions of many new equations. In the 1980s the deeper significance of the tools used in this method - Hirota derivatives and the bilinear form - came to be understood as a key ingredient in Sato's theory and the connections with affine Lie algebras. The main part of this book concerns the more modern version of the method in which solutions are expressed in the form of determinants and pfaffians. While maintaining the original philosophy of using relatively simple mathematics, it has, nevertheless, been influenced by the deeper understanding that came out of the work of the Kyoto school. The book will be essential for all those working in soliton theory Solitons Direkte Methode (DE-588)4705893-6 gnd rswk-swf Soliton (DE-588)4135213-0 gnd rswk-swf Soliton (DE-588)4135213-0 s Direkte Methode (DE-588)4705893-6 s DE-604 Nagai, Atsushi edt trl Nimmo, J. J. C. edt trl Gilson, Claire edt trl Erscheint auch als Druck-Ausgabe 978-0-521-83660-9 https://doi.org/10.1017/CBO9780511543043 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Hirota, Ryogo 1932- The direct method in soliton theory 1. Bilinearization of soliton equations -- 2. Determinants and pfaffians -- 3. Structure of soliton equations -- 4. Backlund transformations -- Afterword -- References -- Index Solitons Direkte Methode (DE-588)4705893-6 gnd Soliton (DE-588)4135213-0 gnd |
| subject_GND | (DE-588)4705893-6 (DE-588)4135213-0 |
| title | The direct method in soliton theory |
| title_alt | Chokusetsuhō ni yoru soriton no sūri |
| title_auth | The direct method in soliton theory |
| title_exact_search | The direct method in soliton theory |
| title_full | The direct method in soliton theory Ryogo Hirota ; translated from Japanese and edited by Atsushi Nagai, Jon Nimmo, and Claire Gilson |
| title_fullStr | The direct method in soliton theory Ryogo Hirota ; translated from Japanese and edited by Atsushi Nagai, Jon Nimmo, and Claire Gilson |
| title_full_unstemmed | The direct method in soliton theory Ryogo Hirota ; translated from Japanese and edited by Atsushi Nagai, Jon Nimmo, and Claire Gilson |
| title_short | The direct method in soliton theory |
| title_sort | the direct method in soliton theory |
| topic | Solitons Direkte Methode (DE-588)4705893-6 gnd Soliton (DE-588)4135213-0 gnd |
| topic_facet | Solitons Direkte Methode Soliton |
| url | https://doi.org/10.1017/CBO9780511543043 |
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