  The aim of this paper is to use correspondence between solutions in the $c=1$
matrix model collective field theory and coupled dilaton-gravity to a massless
scalar field. First, we obtain the incoming and outgoing fluctuations for the
time-dependent backgrounds with the lightlike and spacelike boundaries. In the
case of spacelike boundaries, we have done here for the first time. Then by
using the leg-pole transformations we find corresponding tachyon field in two
dimensional string theory for lightlikes and spacelikes boundary.

High Energy Physics - Theory