New wave solutions of the Yang-Mills equations with axially symmetric sources

Abstract

A class of nontrivial axially symmetric wave solutions to the Yang-Mills equations with SU(2) symmetry is studied. It describes transversal non-Abelian waves propagated at constant phase velocities through axially symmetric sources of Yang-Mills fields along their axes. In the considered case, the Yang-Mills equations are reduced to a system of six nonlinear partial differential equations. These equations are studied for a special class of axially symmetri sources satisfying a differential equation of charge conservation. From them partial differential equations of the first order for only the Yang-Mills field strengths are derived. To investigate these equations, a special method is proposed. As a result, their exact solutions are found. Using them, exact formulas for the field strengths and potentials in the non-Abelian waves under examination are obtained.