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...
Збережено в:
| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2013 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2013
|
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/149219 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862644566049423360 |
|---|---|
| author | Dimakis, A. Müller-Hoissen, F. |
| author_facet | Dimakis, A. Müller-Hoissen, F. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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).
|
| first_indexed | 2025-12-01T09:31:07Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-149219 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-01T09:31:07Z |
| publishDate | 2013 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | 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 |
| spellingShingle | Binary Darboux Transformations in Bidifferential Calculus and Integrable Reductions of Vacuum Einstein Equations Dimakis, A. Müller-Hoissen, F. |
| title | 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_short | 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 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149219 |
| work_keys_str_mv | AT dimakisa binarydarbouxtransformationsinbidifferentialcalculusandintegrablereductionsofvacuumeinsteinequations AT mullerhoissenf binarydarbouxtransformationsinbidifferentialcalculusandintegrablereductionsofvacuumeinsteinequations |