Travelling wave solutions of three-component systems with competition and diffusion

Travelling wave solutions of three-component systems with competition and diffusion in which the first two species diffuse slowly but react fast than the third species are considered. Under the assumption that these systems have two stable equilibrium states, F±, the multiple existence and stability of travelling wave solutions connecting P_ with P+ are shown by using analytical singular perturbation method and the SLEP method. Velocity of a travelling wave solution surely depends on the third species. For the multiple existence of stable solutions, the dependency of its velocity on the third species is important.