Solutions in self-dual gravity constructed via chiral equations

The chiral model for self-dual gravity given by Husain in the context of the chiral equations approach is discussed. A Lie algebra corresponding to a finite dimensional subgroup of the group of symplectic diffeomorphisms is found, and then used for expanding the Lie-algebra-valued connections associated with the chiral model. The self-dual metric can be explicitly given in terms of harmonic maps and in terms of a basis of this subalgebra.