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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 a Iosif S. KRASIL'SHCHIK. Nonlocal Symmetries of Integrable Linearly Degenerate Equations: A Comparative Study. \textit{Theoretical and Mathematical Physics}. New York: Pleiades Publishing, 2018, roč.~196, č.~2, s.~1089-1110. ISSN~0040-5779. Dostupné z: https://dx.doi.org/10.1134/S0040577918080019.
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