  We consider the inhomogeneous decay of an unstable D-brane of bosonic string
theory in a linear dilaton background in a light-cone frame. At the lowest
level, the dynamical equation that describes this process is a generalisation
(that includes nonlocality and time delay) of a reaction-diffusion equation
studied by Fisher (and others). We argue that the equation of motion of the
cubic open string field theory is satisfied at least to the second order when
we start with this `Fisher deformation', a marginal operator which has a simple
pole term in its OPE. We also compute the one-point functions of closed string
operators on the disc in the presence of this deformation.
