Dispersionless Multi-Dimensional Integrable Systems and Related Conformal Structure Generating Equations of Mathematical Physics
Using diffeomorphism group vector fields on C-multiplied tori and the related Lie-algebraic structures, we study multi-dimensional dispersionless integrable systems that describe conformal structure generating equations of mathematical physics. An interesting modification of the devised Lie-algebrai...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2019 |
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Інститут математики НАН України
2019
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/210309 |
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| Cite this: | Dispersionless Multi-Dimensional Integrable Systems and Related Conformal Structure Generating Equations of Mathematical Physics / O.Ye. Hentosh, Ya.A. Prykarpatsky, D. Blackmore, A.K. Prykarpatski // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 30 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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Hentosh, O.Ye. Prykarpatsky, Ya.A. Blackmore, D. Prykarpatski, A.K. 2025-12-05T09:31:54Z 2019 Dispersionless Multi-Dimensional Integrable Systems and Related Conformal Structure Generating Equations of Mathematical Physics / O.Ye. Hentosh, Ya.A. Prykarpatsky, D. Blackmore, A.K. Prykarpatski // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 30 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 17B68; 17B80; 35Q53; 35G25; 35N10; 37K35; 58J70; 58J72; 34A34; 37K05; 37K10 arXiv: 1902.08111 https://nasplib.isofts.kiev.ua/handle/123456789/210309 https://doi.org/10.3842/SIGMA.2019.079 Using diffeomorphism group vector fields on C-multiplied tori and the related Lie-algebraic structures, we study multi-dimensional dispersionless integrable systems that describe conformal structure generating equations of mathematical physics. An interesting modification of the devised Lie-algebraic approach subject to spatial-dimensional invariance and meromorphicity of the related differential-geometric structures is described and applied in proving complete integrability of some conformal structure generating equations. As examples, we analyze the Einstein-Weyl metric equation, the modified Einstein-Weyl metric equation, the Dunajski heavenly equation system, the first and second conformal structure generating equations, and the inverse first Shabat reduction heavenly equation. We also analyze the modified Plebański heavenly equations, the Husain heavenly equation, and the general Monge equation, along with their multi-dimensional generalizations. In addition, we construct superconformal analogs of the Whitham heavenly equation. The authors are cordially indebted to Professors Alexander Balinsky, Maxim Pavlov, and Artur Sergyeyev for useful comments and remarks, especially for elucidating references that were very instrumental in preparing this manuscript. They are also indebted to Professor Anatol Odzijewicz for fruitful and instructive discussions during the XXXVII Workshop on Geometric Methods in Physics held on July 1-7, 2018, in Białowieża, Poland. Thanks are also due to the Department of Physics, Mathematics, and Computer Science of the Krakow University of Technology for a local research grant F-2/370/2018/DS. This work was partly funded by the Ukrainian budget program "Support for the development of priority research areas" (CPCEC 6451230). Last but not least, thanks are due to the referees for carefully reading our work, making insightful remarks, and posing questions that were useful in preparing a revised manuscript. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Dispersionless Multi-Dimensional Integrable Systems and Related Conformal Structure Generating Equations of Mathematical Physics Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| title |
Dispersionless Multi-Dimensional Integrable Systems and Related Conformal Structure Generating Equations of Mathematical Physics |
| spellingShingle |
Dispersionless Multi-Dimensional Integrable Systems and Related Conformal Structure Generating Equations of Mathematical Physics Hentosh, O.Ye. Prykarpatsky, Ya.A. Blackmore, D. Prykarpatski, A.K. |
| title_short |
Dispersionless Multi-Dimensional Integrable Systems and Related Conformal Structure Generating Equations of Mathematical Physics |
| title_full |
Dispersionless Multi-Dimensional Integrable Systems and Related Conformal Structure Generating Equations of Mathematical Physics |
| title_fullStr |
Dispersionless Multi-Dimensional Integrable Systems and Related Conformal Structure Generating Equations of Mathematical Physics |
| title_full_unstemmed |
Dispersionless Multi-Dimensional Integrable Systems and Related Conformal Structure Generating Equations of Mathematical Physics |
| title_sort |
dispersionless multi-dimensional integrable systems and related conformal structure generating equations of mathematical physics |
| author |
Hentosh, O.Ye. Prykarpatsky, Ya.A. Blackmore, D. Prykarpatski, A.K. |
| author_facet |
Hentosh, O.Ye. Prykarpatsky, Ya.A. Blackmore, D. Prykarpatski, A.K. |
| publishDate |
2019 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
Using diffeomorphism group vector fields on C-multiplied tori and the related Lie-algebraic structures, we study multi-dimensional dispersionless integrable systems that describe conformal structure generating equations of mathematical physics. An interesting modification of the devised Lie-algebraic approach subject to spatial-dimensional invariance and meromorphicity of the related differential-geometric structures is described and applied in proving complete integrability of some conformal structure generating equations. As examples, we analyze the Einstein-Weyl metric equation, the modified Einstein-Weyl metric equation, the Dunajski heavenly equation system, the first and second conformal structure generating equations, and the inverse first Shabat reduction heavenly equation. We also analyze the modified Plebański heavenly equations, the Husain heavenly equation, and the general Monge equation, along with their multi-dimensional generalizations. In addition, we construct superconformal analogs of the Whitham heavenly equation.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/210309 |
| citation_txt |
Dispersionless Multi-Dimensional Integrable Systems and Related Conformal Structure Generating Equations of Mathematical Physics / O.Ye. Hentosh, Ya.A. Prykarpatsky, D. Blackmore, A.K. Prykarpatski // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 30 назв. — англ. |
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| first_indexed |
2025-12-07T21:25:06Z |
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2025-12-07T21:25:06Z |
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