On non-Abelian waves repeatedly changing sign at constant phases

In this paper, we study a new class of wave solutions to the SU(2) Yang-Mills equations in the region outside field sources. They represent a significant addition to the wave solutions obtained in our previous publications 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. As a result, we come to a system of ordinary differential equations of the second order for unknown functions. We find a class of solutions to this system of equations, which give new exact non-Abelian wave solutions to the Yang-Mills equations containing any finite number of arbitrary functions dependent of the wave phase. It is shown that the found wave solutions exhibit the following interesting property: Their nonzero field strengths change sign repeatedly when the radial coordinate changes and the wave phase and polar angle are fixed. The main novelty of the present work lies in the found enlarged class of polynomial solutions to the SU(2) Yang-Mills equations describing non-Abelian transverse progressive waves.