Laplace transformation of Lie class \omega=1 overdetermined systems
  In this paper we investigate overdetermined systems of scalar PDEs on the plane with one common characteristic, whose general solution depends on 1 function of 1 variable. We describe linearization of such systems and their integration via Laplace transformation, relating this to Lie's integration theorem and formal theory of PDEs. 
Boris Kruglikov
math.AP math.DG