Seminar talk, 13 September 2017

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Speaker: Joseph Krasil'shchik

Title: 2D reductions of the equation [math]\displaystyle{ u_{yy} = u_{tx} + u_y u_{xx} - u_x u_{xy} }[/math] and their nonlocal symmetries

Abstract:
We consider the 3D equation [math]\displaystyle{ u_{yy} = u_{tx} + u_y u_{xx} - u_x u_{xy} }[/math] and its 2D reductions: (1) [math]\displaystyle{ u_{yy} = (u_y + y) u_{xx} - u_x u_{xy} - 2 }[/math] (which is equivalent to the Gibbons-Tsarev equation) and (2) [math]\displaystyle{ u_{yy} = (u_y + 2x) u_{xx} + (y - u_x) u_{xy} - u_x }[/math]. 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.

Joint work with P. Holba, O. I. Morozov, and P. Vojčák.

References:
arXiv:1707.07645