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@article{30209,
author = {Baran, Hynek and Vojčák, Petr and Morozov, Oleg I. and Krasil'shchik, Iosif S.},
article_location = {New York},
article_number = {2},
doi = {http://dx.doi.org/10.1134/S0040577918080019},
keywords = {partial differential equation; integrable linearly degenerate equation; nonlocal symmetry; recursion operator},
language = {eng},
issn = {0040-5779},
journal = {Theoretical and Mathematical Physics},
title = {Nonlocal Symmetries of Integrable Linearly Degenerate Equations: A Comparative Study},
url = {https://link.springer.com/article/10.1134%2FS0040577918080019},
volume = {196},
year = {2018}
}
TY - JOUR
ID - 30209
AU - Baran, Hynek - Vojčák, Petr - Morozov, Oleg I. - Krasil'shchik, Iosif S.
PY - 2018
TI - Nonlocal Symmetries of Integrable Linearly Degenerate Equations: A Comparative Study
JF - Theoretical and Mathematical Physics
VL - 196
IS - 2
SP - 1089-1110
EP - 1089-1110
PB - Pleiades Publishing
SN - 00405779
KW - partial differential equation
KW - integrable linearly degenerate equation
KW - nonlocal symmetry
KW - recursion operator
UR - https://link.springer.com/article/10.1134%2FS0040577918080019
L2 - https://link.springer.com/article/10.1134%2FS0040577918080019
N2 - We continue the study of Lax integrable equations. We consider four three-dimensional equations: (1) the rdDym equation u(ty) = u(x)u(xy) - u(y)u(xx), (2) the Pavlov equation u(yy) = u(tx) + u(y)u(xx) - u(x)u(xy), (3) the universal hierarchy equation u(yy) = u(t)u(xy) - u(y)u(tx), and (4) the modified Veronese web equation u(ty) = u(t)u(xy) - u(y)u(tx). For each equation, expanding the known Lax pairs in formal series in the spectral parameter, we construct two differential coverings and completely describe the nonlocal symmetry algebras associated with these coverings. For all four pairs of coverings, the obtained Lie algebras of symmetries manifest similar (but not identical) structures; they are (semi)direct sums of the Witt algebra, the algebra of vector fields on the line, and loop algebras, all of which contain a component of finite grading. We also discuss actions of recursion operators on shadows of nonlocal symmetries.
ER -
BARAN, Hynek, Petr VOJČÁK, Oleg I. MOROZOV and Iosif S. KRASIL'SHCHIK. Nonlocal Symmetries of Integrable Linearly Degenerate Equations: A Comparative Study. \textit{Theoretical and Mathematical Physics}. New York: Pleiades Publishing, 2018, vol.~196, No~2, p.~1089-1110. ISSN~0040-5779. Available from: https://dx.doi.org/10.1134/S0040577918080019.
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