J
2019
On symmetries of the Gibbons-Tsarev equation
BARAN, Hynek; Petr BLASCHKE; Michal MARVAN and Iosif S. KRASIL'SHCHIK
Basic information
Original name
On symmetries of the Gibbons-Tsarev equation
Edition
Journal of Geometry and Physics, Amsterdam, Elsevier B.V. 2019, 0393-0440
Other information
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
Impact factor
Impact factor: 1.056
RIV identification code
RIV/47813059:19610/19:A0000042
Organization unit
Mathematical Institute in Opava
EID Scopus
2-s2.0-85066736273
Keywords in English
Gibbons-Tsarev equation; Differential coverings; Nonlocal symmetries; Nonlocal conservation laws; Witt algebra
Tags
International impact, Reviewed
Links
EE2.3.20.0002, research and development project. GBP201/12/G028, research and development project.
In the original language
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.
Displayed: 29/1/2026 22:54