We study the evolution of Bianchi-I space-times filled with a global unidirectional electromagnetic field Fµν interacting with a massless scalar dilatonic field according to the law Ψ(φ)F µν Fµν where Ψ(φ) > 0 is an arbitrary function. A qualitative study, among other results, shows that (i) the volume factor always evolves monotonically, (ii) there exist models becoming isotropic at late times and (iii) the expansion generically starts from a singularity but there can be special models starting from a Killing horizon preceded by a static stage. All three features are confirmed for exact solutions found for the usually considered case Ψ = e 2λφ , λ = const . In particular, isotropizing models are found for |λ| > 1/ √ 3 . In the special case |λ| = 1 , which corresponds to models of string origin, the string metric behaviour is studied and shown to be qualitatively similar to that of the Einstein frame metric.

We consider static, cylindrically symmetric configurations in general relativity coupled to nonlinear electrodynamics (NED) with an arbitrary gauge-invariant Lagrangian of the form Lem = Φ(F ) , F = F αβ F αβ . We study electric and magnetic fields with three possible orientations: radial (R), longitudinal (L) and azimuthal (A), and try to find solitonic stringlike solutions, having a regular axis and a flat metric at large r , with a possible angular defect. Assuming that the function Φ(F ) is regular at small F , it is shown that a regular axis is impossible in R-fields if there is a nonzero effective electric charge and in A-fields if there is a nonzero effective electric current along the axis. Thus solitonic solutions are only possible for purely magnetic R-fields and purely electric A-fields, in cases when Φ(F ) tends to a finite limit at large F . For both R-and A-fields it is shown that the desired large r asymptotic is only possible with a non-Maxwell behaviour of Φ(F ) at small F . For L-fields, solutions with a regular axis are easily obtained (and can be found by quadratures) whereas a desired large r asymptotic is only possible in an exceptional solution; the latter gives rise to solitonic configurations in case Φ(F ) = const · √ F . We give an explicit example of such a solution.