Einstein--Maxwell--Dilaton metrics from three--dimensional Einstein--Weyl structures

A class of time dependent solutions to $(3+1)$ Einstein–Maxwell-dilaton theory with attractive electric force is found from Einstein–Weyl structures in (2+1) dimensions corresponding to dispersionless Kadomtsev–Petviashvili and $SU(\mathrm{\infty })$ Toda equations. These solutions are obtained from time–like Kaluza–Klein reductions of $(3+2)$ solitons.