Contact relative differential invariants for non generic parabolic Monge-Ampère equations (Q941646)

In the present paper the classical problem of contact classification of Monge-Ampère equations is studied. This problem has a long history, starting with S. Lie, G. Darboux and E. Goursat, see the recent monograph [\textit{A. Kushner, V. Lychagin} and \textit{V. Rubtsov}, Contact geometry and nonlinear differential equations. Encyclopedia of Mathematics and Its Applications 101, Cambridge University Press (2007; Zbl 1122.53044)]. This paper is devoted to classification of parabolic equations. The authors characterize in terms of relative invariants when a parabolic Monge-Ampère equation can be brought to one of the forms \(z_{yy}=F(x,y,z,z_x,z_y)\) or \(z_{yy}-2zz_{xy}+z^2z_{xx}=G(x,y,z,z_x,z_y)\).