2D reductions of the equation uyy = utx + uyuxx − uxuxy and their nonlocal symmetries. (21st December 2017) - Holba, P.; Krasil'shchik, I.S.; Morozov, O.I.; Vojčák, P.
Abstract : We consider the 3D equation uyy = utx + uy uxx − ux uxy and its 2D symmetry reductions: (1) uyy = ( uy + y ) uxx − ux uxy − 2 (which is equivalent to the Gibbons-Tsarev equation) and (2) uyy = ( uy + 2 x ) 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.