Seiberg-Witten equations in R 4 : Lie symmetries, particular solutions, integrability

It is shown that the 11-parameter automorphism group of Lie algebra of four-dimensional Euclidean group is a maximal Lie symmetries group of the Seiberg-Witten equations in R 4 . Particular explicit solutions which are invariant under SO(3) subgroups of the maximal Lie symmetries group are constructed. It is established that Seiberg-Witten equations do not possess the Painlevé property. Nevertheless, SO(3) invariant solutions obtained are turned to admit a characteristic singularity structure.