# Seminar talk, 13 September 2017

Title: 2D reductions of the equation ${\displaystyle u_{yy}=u_{tx}+u_{y}u_{xx}-u_{x}u_{xy}}$ and their nonlocal symmetries
We consider the 3D equation ${\displaystyle u_{yy}=u_{tx}+u_{y}u_{xx}-u_{x}u_{xy}}$ and its 2D reductions: (1) ${\displaystyle u_{yy}=(u_{y}+y)u_{xx}-u_{x}u_{xy}-2}$ (which is equivalent to the Gibbons-Tsarev equation) and (2) ${\displaystyle u_{yy}=(u_{y}+2x)u_{xx}+(y-u_{x})u_{xy}-u_{x}}$. 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.