  Reaction-diffusion systems with cross-diffusion terms in addition to, or
instead of, the usual self-diffusion demonstrate interesting features which
motivate their further study. The present work is aimed at designing a toy
reaction-cross-diffusion model with exact solutions in the form of propagating
fronts. We propose a minimal model of this kind which involves two species
linked by cross-diffusion, one of which governed by a linear equation and the
other having a polynomial kinetic term. We classify the resulting exact
propagating front solutions. Some of them have some features of the Fisher-KPP
fronts and some features of the ZFK-Nagumo fronts.
