On self-similar global textures in an expanding universe

We discuss self-similar solutions to O(4) textures in Minkowski space and if flat Friedmann-Robertson-Walker back-grounds. We show that in the Minkowski case there exist no solutions with winding number greater than unity. However, we find besides the known solution with unit winding number also previously unknown solutions corresponding to winding number less than one. The applicability of the non-linear sigma model approximation is discussed. We point out that no spherically symmetric exactly self-similar solutions exist for radiation or matter dominated FRW cosmologies, but we find a way to relax the assumptions of self-similarity that give us approximate solutions valid on intermediate scales.