  We study two systems of reaction diffusion equations with monostable or
bistable type of nonlinearity and with free boundaries. These systems are used
as multi-species competitive model. For two-species models, we prove the
existence of a traveling wave solution which consists of two semi-waves
intersecting at the free boundary. For three-species models, we also prove the
existence of a traveling wave solution which, however, consists of two
semi-waves and one compactly supported wave in between, each intersecting with
its neighbor at the free boundary.
