Multicomponent Burgers and KP Hierarchies, and Solutions from a Matrix Linear System
Via a Cole-Hopf transformation, the multicomponent linear heat hierarchy leads to a multicomponent Burgers hierarchy. We show in particular that any solution of the latter also solves a corresponding multicomponent (potential) KP hierarchy. A generalization of the Cole-Hopf transformation leads to a...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2009 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2009
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/149261 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Multicomponent Burgers and KP Hierarchies, and Solutions from a Matrix Linear System / A. Dimakis, F. Müller-Hoissen // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 52 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862716960332054528 |
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| author | Dimakis, A. Müller-Hoissen, F. |
| author_facet | Dimakis, A. Müller-Hoissen, F. |
| citation_txt | Multicomponent Burgers and KP Hierarchies, and Solutions from a Matrix Linear System / A. Dimakis, F. Müller-Hoissen // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 52 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Via a Cole-Hopf transformation, the multicomponent linear heat hierarchy leads to a multicomponent Burgers hierarchy. We show in particular that any solution of the latter also solves a corresponding multicomponent (potential) KP hierarchy. A generalization of the Cole-Hopf transformation leads to a more general relation between the multicomponent linear heat hierarchy and the multicomponent KP hierarchy. From this results a construction of exact solutions of the latter via a matrix linear system.
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| first_indexed | 2025-12-07T18:08:02Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-149261 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T18:08:02Z |
| publishDate | 2009 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Dimakis, A. Müller-Hoissen, F. 2019-02-19T19:29:49Z 2019-02-19T19:29:49Z 2009 Multicomponent Burgers and KP Hierarchies, and Solutions from a Matrix Linear System / A. Dimakis, F. Müller-Hoissen // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 52 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 37K10; 35Q53 https://nasplib.isofts.kiev.ua/handle/123456789/149261 Via a Cole-Hopf transformation, the multicomponent linear heat hierarchy leads to a multicomponent Burgers hierarchy. We show in particular that any solution of the latter also solves a corresponding multicomponent (potential) KP hierarchy. A generalization of the Cole-Hopf transformation leads to a more general relation between the multicomponent linear heat hierarchy and the multicomponent KP hierarchy. From this results a construction of exact solutions of the latter via a matrix linear system. This paper is a contribution to the Proceedings of the XVIIth International Colloquium on Integrable Systems and Quantum Symmetries (June 19–22, 2008, Prague, Czech Republic). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Multicomponent Burgers and KP Hierarchies, and Solutions from a Matrix Linear System Article published earlier |
| spellingShingle | Multicomponent Burgers and KP Hierarchies, and Solutions from a Matrix Linear System Dimakis, A. Müller-Hoissen, F. |
| title | Multicomponent Burgers and KP Hierarchies, and Solutions from a Matrix Linear System |
| title_full | Multicomponent Burgers and KP Hierarchies, and Solutions from a Matrix Linear System |
| title_fullStr | Multicomponent Burgers and KP Hierarchies, and Solutions from a Matrix Linear System |
| title_full_unstemmed | Multicomponent Burgers and KP Hierarchies, and Solutions from a Matrix Linear System |
| title_short | Multicomponent Burgers and KP Hierarchies, and Solutions from a Matrix Linear System |
| title_sort | multicomponent burgers and kp hierarchies, and solutions from a matrix linear system |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149261 |
| work_keys_str_mv | AT dimakisa multicomponentburgersandkphierarchiesandsolutionsfromamatrixlinearsystem AT mullerhoissenf multicomponentburgersandkphierarchiesandsolutionsfromamatrixlinearsystem |