BARAN, Hynek, Petr BLASCHKE, Michal MARVAN and Iosif S. KRASIL'SHCHIK. On symmetries of the Gibbons-Tsarev equation. Journal of Geometry and Physics. Amsterdam: Elsevier B.V., 2019, vol. 144, October, p. 54-80. ISSN 0393-0440. Available from: https://dx.doi.org/10.1016/j.geomphys.2019.05.011.
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Basic information
Original name On symmetries of the Gibbons-Tsarev equation
Authors BARAN, Hynek (203 Czech Republic, belonging to the institution), Petr BLASCHKE (203 Czech Republic, belonging to the institution), Michal MARVAN (203 Czech Republic, guarantor, belonging to the institution) and Iosif S. KRASIL'SHCHIK (643 Russian Federation).
Edition Journal of Geometry and Physics, Amsterdam, Elsevier B.V. 2019, 0393-0440.
Other information
Original language English
Type of outcome Article in a journal
Field of Study 10101 Pure mathematics
Country of publisher Netherlands
Confidentiality degree is not subject to a state or trade secret
WWW Journal of Geometry and Physics
RIV identification code RIV/47813059:19610/19:A0000042
Organization unit Mathematical Institute in Opava
Doi http://dx.doi.org/10.1016/j.geomphys.2019.05.011
UT WoS 000481564700005
Keywords in English Gibbons-Tsarev equation; Differential coverings; Nonlocal symmetries; Nonlocal conservation laws; Witt algebra
Tags MÚ
Tags International impact, Reviewed
Links EE2.3.20.0002, research and development project. GBP201/12/G028, research and development project.
Changed by Changed by: Mgr. Aleš Ryšavý, učo 28000. Changed: 28/4/2020 19:38.
Abstract
We study the Gibbons-Tsarev equation z(yy) + z(x)z(xy) - z(y)z(xx) + 1 = 0 and, using the known Lax pair, we construct infinite series of conservation laws and the algebra of nonlocal symmetries in the covering associated with these conservation laws. We prove that the algebra is isomorphic to the Witt algebra. Finally, we show that the constructed symmetries are unique in the class of polynomial ones.
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