2D reductions of the equation u(yy) = u(tx) + u(y)u(xx) - u(x)u(xy) and their nonlocal symmetries

@article{30281,
   author = {Holba, Pavel and Vojčák, Petr and Krasil'shchik, Iosif S. and Morozov, Oleg I.},
   article_location = {Abingdon},
   article_number = {1},
   doi = {http://dx.doi.org/10.1080/14029251.2017.1418052},
   keywords = {Partial differential equations; Lax integrable equations; symmetry reductions; nonlocal symmetries; Gibbons-Tsarev equation},
   language = {eng},
   issn = {1402-9251},
   journal = {Journal of Nonlinear Mathematical Physics},
   title = {2D reductions of the equation u(yy) = u(tx) + u(y)u(xx) - u(x)u(xy) and their nonlocal symmetries},
   url = {https://www.tandfonline.com/doi/abs/10.1080/14029251.2017.1418052},
   volume = {24},
   year = {2017}
}

TY  - JOUR
ID  - 30281
AU  - Holba, Pavel - Vojčák, Petr - Krasil'shchik, Iosif S. - Morozov, Oleg I.
PY  - 2017
TI  - 2D reductions of the equation u(yy) = u(tx) + u(y)u(xx) - u(x)u(xy) and their nonlocal symmetries
JF  - Journal of Nonlinear Mathematical Physics
VL  - 24
IS  - 1
SP  - 36-47
EP  - 36-47
PB  - Taylor and Francis Ltd.
SN  - 14029251
KW  - Partial differential equations
KW  - Lax integrable equations
KW  - symmetry reductions
KW  - nonlocal symmetries
KW  - Gibbons-Tsarev equation
UR  - https://www.tandfonline.com/doi/abs/10.1080/14029251.2017.1418052
L2  - https://www.tandfonline.com/doi/abs/10.1080/14029251.2017.1418052
N2  - We consider the 3D equation u_{yy}= u_{tx} + u_y u_{xx} - u_x u_{xy} and its 2D symmetry reductions: (1) u_{yy} = (u_y + y) u_{xx} - u_{x} u_{xy} - 2 (which is equivalent to the Gibbons-Tsarev equation) and (2) u_{yy} = (u_y + 2x) u_{xx} + (y - u_{x}) u{xy} - u_{x}. Using the corresponding reductions of the known Lax pair for the 3D equation, we describe nonlocal symmetries of (1) and (2) and show that the Lie algebras of these symmetries are isomorphic to the Witt algebra.
ER  - 

HOLBA, Pavel, Petr VOJČÁK, Iosif S. KRASIL'SHCHIK and Oleg I. MOROZOV. 2D reductions of the equation u(yy) = u(tx) + u(y)u(xx) - u(x)u(xy) and their nonlocal symmetries. \textit{Journal of Nonlinear Mathematical Physics}. Abingdon: Taylor and Francis Ltd., 2017, vol.~24, No~1, p.~36-47. ISSN~1402-9251. Available from: https://dx.doi.org/10.1080/14029251.2017.1418052.