  Using the relation of a set of nonlinear Langevin equations with
reaction-diffusion processes, we note the existence of a maximal strength of
the noise for the stochastic traveling wave solutions of these equations. Its
determination is obtained using the field-theoretical analysis of
branching-annihilation random walks near the directed percolation transition.
We study its consequence for the stochastic
Fisher-Kolmogorov-Petrovsky-Piscounov equation. For the related Langevin
equation modeling the Quantum Chromodynamic nonlinear evolution of the gluon
density with rapidity, the physical maximal-noise limit may appear before the
directed percolation transition, due to a shift in the traveling-wave speed. In
this regime, an exact solution is known from a coalescence process.
Universality and other open problems and applications are discussed in the
outlook
