Geometry of a quasilinear system of two partial differential equations of the 1st and 2nd order in two functions of two independent variables (Q389126)

This paper concerns systems of two fully nonlinear partial differential equations for two unknown functions \(u\) and \(v\) of two independent variables \(x\) and \(y\). One equation is of first-order, the other one of second-order. The goal is to study integral manifolds which are invariant with respect to point transformations of the type \[ \begin{aligned} &x'= f_1(x,y,u,v),\;y'= f_2(x,y,u,v),\\ &u'= f_3(x,y,u,v),\;v'= f_4(x,y,u,v).\end{aligned} \]