On symmetries of the Gibbons-Tsarev equation

@article{32700,
   author = {Baran, Hynek and Blaschke, Petr and Marvan, Michal and Krasil'shchik, Iosif S.},
   article_location = {Amsterdam},
   article_number = {October},
   doi = {http://dx.doi.org/10.1016/j.geomphys.2019.05.011},
   keywords = {Gibbons-Tsarev equation; Differential coverings; Nonlocal symmetries; Nonlocal conservation laws; Witt algebra},
   language = {eng},
   issn = {0393-0440},
   journal = {Journal of Geometry and Physics},
   title = {On symmetries of the Gibbons-Tsarev equation},
   url = {https://www.sciencedirect.com/science/article/pii/S0393044019301032?via%3Dihub},
   volume = {144},
   year = {2019}
}

TY  - JOUR
ID  - 32700
AU  - Baran, Hynek - Blaschke, Petr - Marvan, Michal - Krasil'shchik, Iosif S.
PY  - 2019
TI  - On symmetries of the Gibbons-Tsarev equation
JF  - Journal of Geometry and Physics
VL  - 144
IS  - October
SP  - 54-80
EP  - 54-80
PB  - Elsevier B.V.
SN  - 03930440
KW  - Gibbons-Tsarev equation
KW  - Differential coverings
KW  - Nonlocal symmetries
KW  - Nonlocal conservation laws
KW  - Witt algebra
UR  - https://www.sciencedirect.com/science/article/pii/S0393044019301032?via%3Dihub
L2  - https://www.sciencedirect.com/science/article/pii/S0393044019301032?via%3Dihub
N2  - 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.
ER  - 

BARAN, Hynek, Petr BLASCHKE, Michal MARVAN and Iosif S. KRASIL'SHCHIK. On symmetries of the Gibbons-Tsarev equation. \textit{Journal of Geometry and Physics}. Amsterdam: Elsevier B.V., vol.~144, October, p.~54-80. ISSN~0393-0440. doi:10.1016/j.geomphys.2019.05.011. 2019.