Directional wave fronts of reaction-diffusion systems

In this work, we study types of undulatory solutions, that we term Directional Wave Fronts (DWF), of non scalar reaction diffusion systems. The DWFs are a natural extension of the well known Plane Wave Fronts (PWFs) solutions. However, the DWFs admit a certain type of boundary conditions. In the present work we show, under suitable conditions on the reaction term, that DWFs also exhibit typical behaviour of PWFs: we just prove the existence of heteroclinic, homoclinic and periodic families of DWFs. Essentially, we require the reaction term to be linearly uncoupled. These results are the generalization of a previous work, concerning the scalar case.