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 so lutions. We employ an infinite symmetry subgroup of CMA(2) to produce a fol iation of the solution space into orbits of solutions with respect to this group and a,corresponding splitting of CMA(2) into an automorphic system an d a resolvent system. Mie propose a new approach to group foliation which i s 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.