Effective Nonlinear Sigma Model Method of Exact Solutions Construction in GR

The effective nonlinear sigma model (NSM) is taken into consideration. Possibility of construction of the effective NSM is discussed. Exact solutions of such a model are presented. The effective NSM of physical chiral fields coupled with plane- and axially-symmetric gravitation fields is constructed. Family of exact solutions of such a system are found out by generalized method of functional parameter.