UDC 530.182:537.813 On Nonstationary Solutions to Yang–Mills Equations A. S. Rabinowitch Moscow State University of Instrument Construction and Information Sciences 20, Stromynka str., Moscow, 107996, Russia We study Yang–Mills fields with SU(2) symmetry generated by classical field sources. <...> We seek new classes of solutions to the examined Yang–Mills equations and find their nontrivial solutions in the case of nonstationary spherically symmetric sources and a wide class of their non-Abelian wave solutions. <...> Key words and phrases: Yang–Mills equations, SU(2) symmetry, classical field sources, nonstationary spherically symmetric solutions, non-Abelian wave solutions. 1. <...> They can be represented as [1, 2] DµFk,µν ≡ ∂µFk,µν +gεklmFl,µνAm µ = (4π/c)Jk,ν, Fk,µν = ∂µAk,ν −∂νAk,µ −gεklmAl,µAm,ν, (1) (2) antisymmetric tensor, ε123 = 1, g is the constant of electroweak interactions, Jk,ν are three four-dimensional vectors of current densities, and ∂µ ≡ ∂/∂xµ, where xµ are orthogonal space-time coordinates of the Minkowsky geometry. <...> Consider Eqs. (1)–(2) in the case of the following field sources: J1,ν = Jν, J2,ν = J3,ν = 0, where µ, ν = 0, 1, 2, 3, k, l, m = 1, 2, 3, Dµ is the Yang–Mills covariant derivative, Al,µ, Fk,µν are potentials and strengths of a Yang–Mills field, respectively, εklm is the (3) where Jν is a classical four-dimensional vector of current densities. <...> This nonlinear theory was studied in our works [3–5], where several classes of exact solutions to Eqs. (1)–(3) were found. <...> Namely, from (3) and the well-known identities for the Yang– Mills covariant derivative Dµ [1, 2] we have that when δ1 = 1, δ2 = δ3 = 0, δkDν[DµFk,µν −(4π/c)Jk,ν] ≡ 0. (4) That is why in Refs. [3–6] one more equation to the Yang–Mills equations (1)–(2) with the field sources of the form (3) was proposed <...>