  In this paper, we study a simple one-dimensional model of reaction-diffusion
with bistable non-linearity and in heterogeneous media. The bistable term
accounts for the so-called Allee effect, and the heterogeneity in the media is
localized. We recall the definition of a transition wave used in similar
situations by well-known authors, and propose an alternative definition for
discussion. We call it generalized traveling wave. As a consequence, we give
new results of pinning in such media, due to Allee effect.
