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. 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. |
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@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.
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