  In the early 2000's, Gourley (2000), Wu et al. (2001), Ashwin et al. (2002)
initiated the study of the positive wavefronts in the delayed
Kolmogorov-Petrovskii-Piskunov-Fisher equation. Since then, this model has
become one of the most popular objects in the studies of traveling waves for
the monostable delayed reaction-diffusion equations. In this paper, we give a
complete solution to the problem of existence and uniqueness of monotone waves
in the KPP-Fisher equation. We show that each monotone traveling wave can be
found via an iteration procedure. The proposed approach is based on the use of
special monotone integral operators (which are different from the usual Wu-Zou
operator) and appropriate upper and lower solutions associated to them. The
analysis of the asymptotic expansions of the eventual traveling fronts at
infinity is another key ingredient of our approach.
