On Transformations of the Rabelo Equations
We study four distinct second-order nonlinear equations of Rabelo which describe pseudospherical surfaces. By transforming these equations to the constant-characteristic form we relate them to some well-studied integrable equations. Two of the Rabelo equations are found to be related to the sine-Gor...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2007 |
| ISSN: | 1815-0659 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2007
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/147226 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | On Transformations of the Rabelo Equations / A. Sakovich, S. Sakovich // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 14 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862715083289788416 |
|---|---|
| author | Sakovich, A. Sakovich, S. |
| author_facet | Sakovich, A. Sakovich, S. |
| citation_txt | On Transformations of the Rabelo Equations / A. Sakovich, S. Sakovich // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 14 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We study four distinct second-order nonlinear equations of Rabelo which describe pseudospherical surfaces. By transforming these equations to the constant-characteristic form we relate them to some well-studied integrable equations. Two of the Rabelo equations are found to be related to the sine-Gordon equation. The other two are transformed into a linear equation and the Liouville equation, and in this way their general solutions are obtained.
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| first_indexed | 2025-12-07T17:55:44Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147226 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T17:55:44Z |
| publishDate | 2007 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Sakovich, A. Sakovich, S. 2019-02-13T19:30:06Z 2019-02-13T19:30:06Z 2007 On Transformations of the Rabelo Equations / A. Sakovich, S. Sakovich // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 14 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 35Q58; 35Q53; 35C05 https://nasplib.isofts.kiev.ua/handle/123456789/147226 We study four distinct second-order nonlinear equations of Rabelo which describe pseudospherical surfaces. By transforming these equations to the constant-characteristic form we relate them to some well-studied integrable equations. Two of the Rabelo equations are found to be related to the sine-Gordon equation. The other two are transformed into a linear equation and the Liouville equation, and in this way their general solutions are obtained. This paper is a contribution to the Proceedings of the Seventh International Conference “Symmetry in Nonlinear Mathematical Physics” (June 24–30, 2007, Kyiv, Ukraine). The authors are grateful to Professors N.H. Ibragimov, A.V. Mikhailov and P.J. Olver for their comments on equation (33), and to the anonymous referee who suggested reference [5]. A.S. is grateful to the Organizing Committee of the Seventh International Conference “Symmetry in Nonlinear Mathematical Physics” (June 24–30, 2007, Kyiv) and ICTP Of fice of External Activities for travel and local support in participating the conference. The work of S.S. was supported in part by the Belarusian Republican Foundation for Fundamental Research. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications On Transformations of the Rabelo Equations Article published earlier |
| spellingShingle | On Transformations of the Rabelo Equations Sakovich, A. Sakovich, S. |
| title | On Transformations of the Rabelo Equations |
| title_full | On Transformations of the Rabelo Equations |
| title_fullStr | On Transformations of the Rabelo Equations |
| title_full_unstemmed | On Transformations of the Rabelo Equations |
| title_short | On Transformations of the Rabelo Equations |
| title_sort | on transformations of the rabelo equations |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147226 |
| work_keys_str_mv | AT sakovicha ontransformationsoftherabeloequations AT sakovichs ontransformationsoftherabeloequations |