  We discuss a general iterative procedure for constructing time dependent
solutions in open string theory describing rolling of a generic tachyon field
away from its maximum. These solutions are characterized by two parameters
labelling the initial position and velocity of the tachyon field, but one of
these parameters can be removed by using time translation symmetry. The Wick
rotated version of the resulting one parameter family of inequivalent solutions
describes a one parameter family of boundary conformal field theories, each
member of which is related to the boundary conformal field theory describing
the original D-brane system by a nearly marginal deformation. We apply this
technique to construct a time dependent solution on a D-brane in bosonic string
theory which can be interpreted as the creation of a lower dimensional brane
during the decay of an unstable D-brane.
