S.Duzhin
Infinitesimal Classification of First Order Systems of Two Partial
Differential Equations In Two Variables.
We give a classification of symbols of partial differential systems
that consist of two equations imposed on two functions in two independent
variables, with respect to the natural action of the group of linear
changes of dependent and independent variables.
The classification turns out to be finite, consisting of 5 types in the real
case and of 4 types in the complex case. Apart from the elliptic, parabolic
and hyperbolic types constituting the well-known classification of second
order equations for a function $u(x,y)$, in the present case we also have
two non-equivalent degenerate types.