Clifford Algebra Derivations of Tau-Functions for Two-Dimensional Integrable Models with Positive and Negative Flows
We use a Grassmannian framework to define multi-component tau functions as expectation values of certain multi-component Fermi operators satisfying simple bilinear commutation relations on Clifford algebra. The tau functions contain both positive and negative flows and are shown to satisfy the 2n-co...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2007 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут математики НАН України
2007
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/147787 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Clifford Algebra Derivations of Tau-Functions for Two-Dimensional Integrable Models with Positive and Negative Flows / H. Aratyn, J. van de Leur // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 15 назв. — англ. |
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Aratyn, H. van de Leur, J. 2019-02-16T08:10:09Z 2019-02-16T08:10:09Z 2007 Clifford Algebra Derivations of Tau-Functions for Two-Dimensional Integrable Models with Positive and Negative Flows / H. Aratyn, J. van de Leur // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 15 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 11E88; 17B67; 22E67; 37K10 https://nasplib.isofts.kiev.ua/handle/123456789/147787 We use a Grassmannian framework to define multi-component tau functions as expectation values of certain multi-component Fermi operators satisfying simple bilinear commutation relations on Clifford algebra. The tau functions contain both positive and negative flows and are shown to satisfy the 2n-component KP hierarchy. The hierarchy equations can be formulated in terms of pseudo-differential equations for n × n matrix wave functions derived in terms of tau functions. These equations are cast in form of Sato-Wilson relations. A reduction process leads to the AKNS, two-component Camassa-Holm and Cecotti-Vafa models and the formalism provides simple formulas for their solutions. This paper is a contribution to the Vadim Kuznetsov Memorial Issue “Integrable Systems and Related Topics”. This work has been partially supported by the European Union through the FP6 Marie Curie RTN ENIGMA (Contract number MRTN-CT-2004-5652) and the European Science Foundation Program MISGAM. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Clifford Algebra Derivations of Tau-Functions for Two-Dimensional Integrable Models with Positive and Negative Flows Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Clifford Algebra Derivations of Tau-Functions for Two-Dimensional Integrable Models with Positive and Negative Flows |
| spellingShingle |
Clifford Algebra Derivations of Tau-Functions for Two-Dimensional Integrable Models with Positive and Negative Flows Aratyn, H. van de Leur, J. |
| title_short |
Clifford Algebra Derivations of Tau-Functions for Two-Dimensional Integrable Models with Positive and Negative Flows |
| title_full |
Clifford Algebra Derivations of Tau-Functions for Two-Dimensional Integrable Models with Positive and Negative Flows |
| title_fullStr |
Clifford Algebra Derivations of Tau-Functions for Two-Dimensional Integrable Models with Positive and Negative Flows |
| title_full_unstemmed |
Clifford Algebra Derivations of Tau-Functions for Two-Dimensional Integrable Models with Positive and Negative Flows |
| title_sort |
clifford algebra derivations of tau-functions for two-dimensional integrable models with positive and negative flows |
| author |
Aratyn, H. van de Leur, J. |
| author_facet |
Aratyn, H. van de Leur, J. |
| publishDate |
2007 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
We use a Grassmannian framework to define multi-component tau functions as expectation values of certain multi-component Fermi operators satisfying simple bilinear commutation relations on Clifford algebra. The tau functions contain both positive and negative flows and are shown to satisfy the 2n-component KP hierarchy. The hierarchy equations can be formulated in terms of pseudo-differential equations for n × n matrix wave functions derived in terms of tau functions. These equations are cast in form of Sato-Wilson relations. A reduction process leads to the AKNS, two-component Camassa-Holm and Cecotti-Vafa models and the formalism provides simple formulas for their solutions.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/147787 |
| citation_txt |
Clifford Algebra Derivations of Tau-Functions for Two-Dimensional Integrable Models with Positive and Negative Flows / H. Aratyn, J. van de Leur // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 15 назв. — англ. |
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AT aratynh cliffordalgebraderivationsoftaufunctionsfortwodimensionalintegrablemodelswithpositiveandnegativeflows AT vandeleurj cliffordalgebraderivationsoftaufunctionsfortwodimensionalintegrablemodelswithpositiveandnegativeflows |
| first_indexed |
2025-12-07T16:42:47Z |
| last_indexed |
2025-12-07T16:42:47Z |
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1850868516635279360 |