KP Trigonometric Solitons and an Adelic Flag Manifold
We show that the trigonometric solitons of the KP hierarchy enjoy a differential-difference bispectral property, which becomes transparent when translated on two suitable spaces of pairs of matrices satisfying certain rank one conditions. The result can be seen as a non-self-dual illustration of Wil...
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| Дата: | 2007 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2007
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/147795 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | KP Trigonometric Solitons and an Adelic Flag Manifold / L. Haine // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 21 назв. — англ. |
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irk-123456789-1477952019-02-17T01:27:32Z KP Trigonometric Solitons and an Adelic Flag Manifold Haine, L. We show that the trigonometric solitons of the KP hierarchy enjoy a differential-difference bispectral property, which becomes transparent when translated on two suitable spaces of pairs of matrices satisfying certain rank one conditions. The result can be seen as a non-self-dual illustration of Wilson's fundamental idea [Invent. Math. 133 (1998), 1-41] for understanding the (self-dual) bispectral property of the rational solutions of the KP hierarchy. It also gives a bispectral interpretation of a (dynamical) duality between the hyperbolic Calogero-Moser system and the rational Ruijsenaars-Schneider system, which was first observed by Ruijsenaars [Comm. Math. Phys. 115 (1988), 127-165]. 2007 Article KP Trigonometric Solitons and an Adelic Flag Manifold / L. Haine // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 21 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 35Q53; 37K10 http://dspace.nbuv.gov.ua/handle/123456789/147795 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
We show that the trigonometric solitons of the KP hierarchy enjoy a differential-difference bispectral property, which becomes transparent when translated on two suitable spaces of pairs of matrices satisfying certain rank one conditions. The result can be seen as a non-self-dual illustration of Wilson's fundamental idea [Invent. Math. 133 (1998), 1-41] for understanding the (self-dual) bispectral property of the rational solutions of the KP hierarchy. It also gives a bispectral interpretation of a (dynamical) duality between the hyperbolic Calogero-Moser system and the rational Ruijsenaars-Schneider system, which was first observed by Ruijsenaars [Comm. Math. Phys. 115 (1988), 127-165]. |
| format |
Article |
| author |
Haine, L. |
| spellingShingle |
Haine, L. KP Trigonometric Solitons and an Adelic Flag Manifold Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Haine, L. |
| author_sort |
Haine, L. |
| title |
KP Trigonometric Solitons and an Adelic Flag Manifold |
| title_short |
KP Trigonometric Solitons and an Adelic Flag Manifold |
| title_full |
KP Trigonometric Solitons and an Adelic Flag Manifold |
| title_fullStr |
KP Trigonometric Solitons and an Adelic Flag Manifold |
| title_full_unstemmed |
KP Trigonometric Solitons and an Adelic Flag Manifold |
| title_sort |
kp trigonometric solitons and an adelic flag manifold |
| publisher |
Інститут математики НАН України |
| publishDate |
2007 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147795 |
| citation_txt |
KP Trigonometric Solitons and an Adelic Flag Manifold / L. Haine // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 21 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT hainel kptrigonometricsolitonsandanadelicflagmanifold |
| first_indexed |
2023-05-20T17:28:33Z |
| last_indexed |
2023-05-20T17:28:33Z |
| _version_ |
1796153389212499968 |