Group foliation approach to the complex Monge-Ampere equation

We apply the group foliation method to find noninvariant solutions of the c omplex Monge-Ampere equation (CMA(2)). We use the infinite symmetry subgrou p of the CMA(2) to foliate the solution space into orbits of solutions with respect to this group and correspondingly split the CMA(2) into an automor phic system and a resolvent system. We propose a new approach to group foli ation based on the commutator algebra of operators of invariant differentia tion. This algebra together with Jacobi identities provides the commutator representation of the resolvent system. For solving the resolvent system, w e propose symmetry reduction, which allows deriving reduced resolving equat ions.