Spherically-symmetric non-linear sigma model: the exact solutions obtained with isometrical embedding method

The method to generate exact cosmological solutions in the frame of the spherically-symmetric non-linear sigma model offered in the present paper. This method is based on the isometrical embeddings of the target space (non-linear sigma-model fields chiral space) into space-time. Also the method application to two- and three-component chiral spaces embedded into space-time was considered. The exact cosmological solutions were obtained in the frame of the several special cases of the two- and three-component spherical-symmetric non-linear sigma-model. The obtained cosmological solutions were also investigated.