2D reductions of the equation uyy = utx + uyuxx − uxuxy and their nonlocal symmetries
- https://doi.org/10.1080/14029251.2017.1418052How to use a DOI?
- Partial differential equations, Lax integrable equations, symmetry reductions, nonlocal symmetries, Gibbons-Tsarev equation
We consider the 3D equation uyy = utx + uyuxx − uxuxy and its 2D symmetry reductions: (1) uyy = (uy + y) uxx − uxuxy − 2 (which is equivalent to the Gibbons-Tsarev equation) and (2) uyy = (uy + 2x)uxx + (y − ux)uxy − ux. 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.
- © 2017 The Authors. Published by Atlantis Press and Taylor & Francis
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Cite this article
TY - JOUR AU - P. Holba AU - I.S. Krasil'shchik AU - O.I. Morozov AU - P. Vojčák PY - 2021 DA - 2021/01 TI - 2D reductions of the equation uyy = utx + uyuxx − uxuxy and their nonlocal symmetries JO - Journal of Nonlinear Mathematical Physics SP - 36 EP - 47 VL - 24 IS - Supplement 1 SN - 1776-0852 UR - https://doi.org/10.1080/14029251.2017.1418052 DO - https://doi.org/10.1080/14029251.2017.1418052 ID - Holba2021 ER -