k-Dirac operator and the Cartan-Kahler theorem for weighted differential   operators
  The k-Dirac operator is a differential operator which is natural to geometric structure of a parabolic type. We will give a set of initial conditions for this operator. In the proof of the claim we will need to adapt some parts from the theory of exterior differential systems to the setting of weighted differential operators. 
Tomas Salac
math.DG