Binary Darboux Transformations in Bidifferential Calculus and Integrable Reductions of Vacuum Einstein Equations
We present a general solution-generating result within the bidifferential calculus approach to integrable partial differential and difference equations, based on a binary Darboux-type transformation. This is then applied to the non-autonomous chiral model, a certain reduction of which is known to ap...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2013 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут математики НАН України
2013
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/149219 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Binary Darboux Transformations in Bidifferential Calculus and Integrable Reductions of Vacuum Einstein Equations / A. Dimakis, F. Müller-Hoissen // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 80 назв. — англ. |
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Dimakis, A. Müller-Hoissen, F. 2019-02-19T18:58:49Z 2019-02-19T18:58:49Z 2013 Binary Darboux Transformations in Bidifferential Calculus and Integrable Reductions of Vacuum Einstein Equations / A. Dimakis, F. Müller-Hoissen // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 80 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 37K10; 16E45 DOI: http://dx.doi.org/10.3842/SIGMA.2013.009 https://nasplib.isofts.kiev.ua/handle/123456789/149219 We present a general solution-generating result within the bidifferential calculus approach to integrable partial differential and difference equations, based on a binary Darboux-type transformation. This is then applied to the non-autonomous chiral model, a certain reduction of which is known to appear in the case of the D-dimensional vacuum Einstein equations with D−2 commuting Killing vector fields. A large class of exact solutions is obtained, and the aforementioned reduction is implemented. This results in an alternative to the well-known Belinski-Zakharov formalism. We recover relevant examples of space-times in dimensions four (Kerr-NUT, Tomimatsu-Sato) and five (single and double Myers-Perry black holes, black saturn, bicycling black rings). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Binary Darboux Transformations in Bidifferential Calculus and Integrable Reductions of Vacuum Einstein Equations Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Binary Darboux Transformations in Bidifferential Calculus and Integrable Reductions of Vacuum Einstein Equations |
| spellingShingle |
Binary Darboux Transformations in Bidifferential Calculus and Integrable Reductions of Vacuum Einstein Equations Dimakis, A. Müller-Hoissen, F. |
| title_short |
Binary Darboux Transformations in Bidifferential Calculus and Integrable Reductions of Vacuum Einstein Equations |
| title_full |
Binary Darboux Transformations in Bidifferential Calculus and Integrable Reductions of Vacuum Einstein Equations |
| title_fullStr |
Binary Darboux Transformations in Bidifferential Calculus and Integrable Reductions of Vacuum Einstein Equations |
| title_full_unstemmed |
Binary Darboux Transformations in Bidifferential Calculus and Integrable Reductions of Vacuum Einstein Equations |
| title_sort |
binary darboux transformations in bidifferential calculus and integrable reductions of vacuum einstein equations |
| author |
Dimakis, A. Müller-Hoissen, F. |
| author_facet |
Dimakis, A. Müller-Hoissen, F. |
| publishDate |
2013 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
We present a general solution-generating result within the bidifferential calculus approach to integrable partial differential and difference equations, based on a binary Darboux-type transformation. This is then applied to the non-autonomous chiral model, a certain reduction of which is known to appear in the case of the D-dimensional vacuum Einstein equations with D−2 commuting Killing vector fields. A large class of exact solutions is obtained, and the aforementioned reduction is implemented. This results in an alternative to the well-known Belinski-Zakharov formalism. We recover relevant examples of space-times in dimensions four (Kerr-NUT, Tomimatsu-Sato) and five (single and double Myers-Perry black holes, black saturn, bicycling black rings).
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/149219 |
| citation_txt |
Binary Darboux Transformations in Bidifferential Calculus and Integrable Reductions of Vacuum Einstein Equations / A. Dimakis, F. Müller-Hoissen // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 80 назв. — англ. |
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2025-12-01T09:31:07Z |
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