  Reaction-diffusion equations with suitable boundary conditions have special
propagating solutions which very closely resemble the moving interfaces in a
first order transition. We show that the dynamics of chiral order parameter for
chiral symmetry breaking transition in heavy-ion collisions, with dissipative
dynamics, is governed by one such equation, specifically, the Newell-Whitehead
equation. Further, required boundary conditions are automatically satisfied due
to the geometry of the collision. The chiral transition is, therefore,
completed by a propagating interface, exactly as for a first order transition,
even though the transition actually is a crossover for relativistic heavy-ion
collisions. Same thing also happens when we consider the initial
confinement-deconfinement transition with Polyakov loop order parameter. The
resulting equation, again with dissipative dynamics, can then be identified
with the reaction-diffusion equation known as the Fitzhugh-Nagumo equation
which is used in population genetics. We discuss the implications of these
results for heavy-ion collisions. We also discuss possible extensions for the
case of early universe.
