Application of the group foliation method to the complex Monge-Ampere equation

We apply the method of group foliation to the complex Monge-Ampere equation (CMA(2)) to establish a regular framework for finding its non-invariant solutions. We employ an infinite symmetry subgroup of CMA(2) to produce a foliation of the solution space into orbits of solutions with respect to this group and a,corresponding splitting of CMA(2) into an automorphic system and a resolvent system. Mie propose a new approach to group foliation which is based on the commutator algebra of operators of invariant differentiation. This algebra together with its Jacobi identities provides the commutator representation of the resolvent system.