Reductions of the Universal Hierarchy and rdDym Equations and Their Symmetry Properties

@article{30482,
   author = {Holba, Pavel and Vojčák, Petr and Krasil'shchik, Iosif S. and Morozov, Oleg I.},
   article_location = {New York},
   article_number = {5},
   doi = {http://dx.doi.org/10.1134/S1995080218050086},
   keywords = {Partial differential equations; Lax integrable equations; symmetry reductions; nonlocal symmetries; universal hierarchy equation; rdDym equation},
   language = {eng},
   issn = {1995-0802},
   journal = {Lobachevskii Journal of Mathematics},
   title = {Reductions of the Universal Hierarchy and rdDym Equations and Their Symmetry Properties},
   url = {https://link.springer.com/article/10.1134%2FS1995080218050086},
   volume = {39},
   year = {2018}
}

TY  - JOUR
ID  - 30482
AU  - Holba, Pavel - Vojčák, Petr - Krasil'shchik, Iosif S. - Morozov, Oleg I.
PY  - 2018
TI  - Reductions of the Universal Hierarchy and rdDym Equations and Their Symmetry Properties
JF  - Lobachevskii Journal of Mathematics
VL  - 39
IS  - 5
SP  - 673-681
EP  - 673-681
PB  - Pleiades Publishing
SN  - 19950802
KW  - Partial differential equations
KW  - Lax integrable equations
KW  - symmetry reductions
KW  - nonlocal symmetries
KW  - universal hierarchy equation
KW  - rdDym equation
UR  - https://link.springer.com/article/10.1134%2FS1995080218050086
L2  - https://link.springer.com/article/10.1134%2FS1995080218050086
N2  - We consider the equations u_{yy}= u_y u_{xx} - (u_x+ u) u_{xy} + u_x u_y , u_{yy} = (u_x+ x) u_{xy} - (u_{xx} + 2) u_y that arise as reductions of the universal hierarchy and rdDym equations, respectively, and describe the Lie algebras of nonlocal symmetries in the infinite-dimensional coverings naturally associated to these equations.
ER  - 

HOLBA, Pavel, Petr VOJČÁK, Iosif S. KRASIL'SHCHIK and Oleg I. MOROZOV. Reductions of the Universal Hierarchy and rdDym Equations and Their Symmetry Properties. \textit{Lobachevskii Journal of Mathematics}. New York: Pleiades Publishing, 2018, vol.~39, No~5, p.~673-681. ISSN~1995-0802. Available from: https://dx.doi.org/10.1134/S1995080218050086.