On Transformations of the Rabelo Equations

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Фізико-технічні та математичні науки
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Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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Symmetry, Integrability and Geometry: Methods and Applications, 2007, том 3
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Symmetry, Integrability and Geometry: Methods and Applications, 2007, том 3, випуск за цей рік
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dc.contributor.author	Sakovich, A.
dc.contributor.author	Sakovich, S.
dc.date.accessioned	2019-02-13T19:30:06Z
dc.date.available	2019-02-13T19:30:06Z
dc.date.issued	2007
dc.identifier.citation	On Transformations of the Rabelo Equations / A. Sakovich, S. Sakovich // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 14 назв. — англ.	uk_UA
dc.identifier.issn	1815-0659
dc.identifier.other	2000 Mathematics Subject Classification: 35Q58; 35Q53; 35C05
dc.identifier.uri	http://dspace.nbuv.gov.ua/handle/123456789/147226
dc.description.abstract	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.	uk_UA
dc.description.sponsorship	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.	uk_UA
dc.language.iso	en	uk_UA
dc.publisher	Інститут математики НАН України	uk_UA
dc.relation.ispartof	Symmetry, Integrability and Geometry: Methods and Applications
dc.title	On Transformations of the Rabelo Equations	uk_UA
dc.type	Article	uk_UA
dc.status	published earlier	uk_UA