Symmetry reduction and exact solutions of the yang-mills equations

Abstract

We present a detailed account of symmetry properties of SU(2) Yang-Mills equations. Using a subgroup structure of the Poincar´e group P(1, 3) we have constructed all P(1, 3)-inequivalent ansatzes for the Yang-Mills field which are invariant under the three-dimensional subgroups of the Poincar´e group. With the aid of these ansatzes reduction of Yang-Mills equations to systems of ordinary differential equations is carried out and wide families of their exact solutions are constructed. © 1995 by Mathematical Ukraina Publisher.