  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
$SU(\infty)$ Toda equations. These solutions are obtained from time--like
Kaluza--Klein reductions of $(3+2)$ solitons.
