Exact solutions of $G$-invariant chiral equations

A method is suggested for solving the chiral equations $(\alpha g_{,z}g^{-1})_{,\bar z}+(\alpha g_{,z}g^{-1})_{,z}=0$ where $g$ belongs to some Lie group $G$. The solution is written out in terms of harmonic maps. The method can be used even for some infinite-dimensional Lie groups.