  The position of an invasion front, propagating into an unstable state,
fluctuates because of the shot noise coming from the discreteness of reacting
particles and stochastic character of the reactions and diffusion. A recent
macroscopic theory [Meerson and Sasorov, Phys. Rev. E 84, 030101(R) (2011)]
yields the probability of observing, during a long time, an unusually slow
front. The theory is formulated as an effective classical Hamiltonian field
theory which operates with the density field and the conjugate "momentum"
field. Further, the theory assumes that the most probable density field history
of an unusually slow front represents, up to small corrections, a traveling
front solution of the Hamilton equations. Here we verify this assumption by
solving the Hamilton equations numerically for models belonging to the directed
percolation universality class.
