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

Emergence of fluctuating traveling front solutions in macroscopic theory of noisy invasion fronts