2D reductions of the equation uyy = utx + uyuxx - uₓuxy and their nonlocal symmetries
Holba, P. · Krasil'shchik, I. S. · Morozov, O. I. · Vojcak, P.
Original · EN
We consider the 3D equation uyy = utx + uyuxx - uₓuxy and its 2D 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 reduction 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.
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