  Our interest here is to find the invader in a two species, diffusive and
competitive Lotka-Volterra system in the particular case of travelling wave
solutions. We investigate the role of diffusion in homogeneous domains. We
might expect a priori two different cases: strong interspecific competition and
weak interspecific competition. In this paper, we study the first one and
obtain a clear conclusion: the invading species is, up to a fixed
multiplicative constant, the more diffusive one.
