On the Linearization Covering Technique and Its Application to Integrable Nonlinear Differential Systems
In this letter, I analyze a covering jet manifold scheme, its relation to the invariant theory of the associated vector fields, and applications to the Lax-Sato-type integrability of nonlinear dispersionless differential systems. The related contact geometry linearization covering scheme is also dis...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2018 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2018
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/209441 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | On the Linearization Covering Technique and its Application to Integrable Nonlinear Differential Systems / A.K. Prykarpatski // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 32 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862640364475645952 |
|---|---|
| author | Prykarpatski, A.K. |
| author_facet | Prykarpatski, A.K. |
| citation_txt | On the Linearization Covering Technique and its Application to Integrable Nonlinear Differential Systems / A.K. Prykarpatski // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 32 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | In this letter, I analyze a covering jet manifold scheme, its relation to the invariant theory of the associated vector fields, and applications to the Lax-Sato-type integrability of nonlinear dispersionless differential systems. The related contact geometry linearization covering scheme is also discussed. The devised techniques are demonstrated for such nonlinear Lax-Sato integrable equations as Gibbons-Tsarev, ABC, Manakov-Santini, and the differential Toda singular manifold equations.
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| first_indexed | 2025-12-01T02:50:20Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-209441 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-01T02:50:20Z |
| publishDate | 2018 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Prykarpatski, A.K. 2025-11-21T18:54:41Z 2018 On the Linearization Covering Technique and its Application to Integrable Nonlinear Differential Systems / A.K. Prykarpatski // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 32 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 17B68; 17B80; 35Q53; 35G25; 35N10; 37K35; 58J70; 58J72; 34A34; 37K05; 37K10 arXiv: 1801.07312 https://nasplib.isofts.kiev.ua/handle/123456789/209441 https://doi.org/10.3842/SIGMA.2018.023 In this letter, I analyze a covering jet manifold scheme, its relation to the invariant theory of the associated vector fields, and applications to the Lax-Sato-type integrability of nonlinear dispersionless differential systems. The related contact geometry linearization covering scheme is also discussed. The devised techniques are demonstrated for such nonlinear Lax-Sato integrable equations as Gibbons-Tsarev, ABC, Manakov-Santini, and the differential Toda singular manifold equations. The author cordially thanks Professors M. Blaszak, B. Szablikowski, and J. Cieślinski for useful discussions of the results during the International Conference in Functional Analysis dedicated to the 125th anniversary of Stefan Banach held on 18–23 September 2017 in Lviv, Ukraine. He is also greatly indebted to Professors V.E. Zakharov (University of Arizona, Tucson) and J. Szmigelski University of Saskatchewan, Saskatoon) for their interest in the work and instructive discussions during the XXXV Workshop on Geometric Methods in Physics, held in Białowieża, Poland. The author is grateful to Professor B. Kruglikov (University of Tromsø, Norway) for his interest in the work and for mentioning some misprints and important references, which were very helpful in preparing the manuscript. He is also indebted to the referees for their remarks and instrumental suggestions. Last but not least, thanks go to the Department of Mathematical Sciences of NJIT (Newark, NJ, USA) for the invitation to visit NJIT during the Summer Semester of 2017, where an essential part of this paper was completed. Local support from the Institute of Mathematics at the Kraków University of Technology is also much appreciated. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications On the Linearization Covering Technique and Its Application to Integrable Nonlinear Differential Systems Article published earlier |
| spellingShingle | On the Linearization Covering Technique and Its Application to Integrable Nonlinear Differential Systems Prykarpatski, A.K. |
| title | On the Linearization Covering Technique and Its Application to Integrable Nonlinear Differential Systems |
| title_full | On the Linearization Covering Technique and Its Application to Integrable Nonlinear Differential Systems |
| title_fullStr | On the Linearization Covering Technique and Its Application to Integrable Nonlinear Differential Systems |
| title_full_unstemmed | On the Linearization Covering Technique and Its Application to Integrable Nonlinear Differential Systems |
| title_short | On the Linearization Covering Technique and Its Application to Integrable Nonlinear Differential Systems |
| title_sort | on the linearization covering technique and its application to integrable nonlinear differential systems |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/209441 |
| work_keys_str_mv | AT prykarpatskiak onthelinearizationcoveringtechniqueanditsapplicationtointegrablenonlineardifferentialsystems |