  e study the minimal wave speed and the asymptotics of the traveling wave
solutions of a competitive Lotka Volterra system. The existence of the
traveling wave solutions is derived by monotone iteration. The asymptotic
behaviors of the wave solutions are derived by comparison argument and the
exponential dichotomy, which seems to be the key to understand the geometry and
the stability of the wave solutions. Also the uniqueness and the monotonicity
of the waves are investigated via a generalized sliding domain method.
