Conformal symmetry and new exact solutions ofSU 2 Yang-Mills theory

Conditional symmetry and new classical solutions of the Yang-Mills equations

“…The reason is that all famous mathematical models of elementary particles such as solitons, instantons, merons are quite simply particular solutions of some nonlinear partial differential equations. A natural approach to construction of particular solutions of YMEs (1) is to utilize their symmetry properties in the way as it is done in [9,10,16] (see, also [15], where the reduction of the Euclidean self-dual YMEs is considered). The apparatus of the theory of Lie transformation groups makes it possible to reduce system of partial differential equations (PDEs) (1) to systems of nonlinear ordinary differential equations (ODEs) by using special ansätze (invariant solutions) [10,18,20].…”

On Poincaré-Invariant Reduction and Exact Solutions of the Yang-Mills Equations

“…Symmetry properties of YME were used and some new exact solutions of equation 1were obtained by W. Fushchych and W.Shtelen in [7] (see also [3]).…”

Symmetry and Exact Solutions of the Maxwell and SU(2) Yang–Mills Equations

“…Note that the conformal group Cð1; 3Þ generated by the infinitesimal operators (27) acts in the space of independent variables R 1;3 only. That is why the basis operators of the algebra c ð1Þ ð1; 3Þ act in the space of dependent variables R q as zero operators.…”

“…To the best of our knowledge, the first paper devoted to symmetry reduction of the SUð2Þ Yang-Mills equations in Minkowski space has been published by Fushchych and Shtelen [27] (see also Ref. 21).…”

“…To the best of our knowledge, the first paper devoted to symmetry reduction of the SU(2) Yang-Mills equations in the Minkowski space has been published by Fushchych and Shtelen [27] (see, also, [21]). They use two conformally-invariant ansatzes in order to perform reduction of equations (1.1) to systems of ordinary differential equations.…”