On a wide class of solutions of SU(2) Yang–Mills equations describing non-Abelian progressive waves

In this paper, wave solutions to the classical Yang-Mills equations with SU(2) symmetry are investigated in the region outside field sources. They represent a significant generalization of the solutions found in our previous publication describing non-Abelian transverse progressive waves propagating in the direction of the Cartesian z-axis. In the new paper, wave solutions to the considered system of nonlinear partial differential equations are sought in a special form. In it, the unknown functions are presented as some complex series and for their coefficients, depending on the wave phase, a system of recurrence relations is obtained. This paper proves that in the examined region, the considered complex series are absolutely convergent. They allow us to determine a wide class of non-Abelian wave solutions to the Yang-Mills equations. In addition, exact wave solutions in closed form are found, which describe the asymptotic behavior of the considered non-Abelian wave solutions for large distances from the z-axis.