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KP Trigonometric Solitons and an Adelic Flag Manifold

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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Main Author: Haine, L.
Format: Article
Language:English
Published: Інститут математики НАН України 2007
Series:Symmetry, Integrability and Geometry: Methods and Applications
Online Access:http://dspace.nbuv.gov.ua/handle/123456789/147795
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spelling 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
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