  We generalize the reaction-diffusion model A + B -> 0 in order to study the
impact of an excess of A (or B) at the reaction front. We provide an exact
solution of the model, which shows that linear response breaks down: the
average displacement of the reaction front grows as the square-root of the
imbalance. We argue that this model provides a highly simplified but generic
framework to understand the square-root impact of large orders in financial
markets.
