Traveling wave solutions of competitive models with free boundaries

We study two systems of reaction diffusion equations with monostable or bistable type of nonlinearitiesand with free boundaries. These systems are used as multi-species competitive model.For two-species models, we prove the existence of traveling wave solutions, each of which consistsof two semi-waves intersecting at the free boundary.For three-species models, we also obtain some traveling wave solutions. In this case, however, everytraveling wave solution consists oftwo semi-waves and one compactly supported wave in between, each intersecting with its neighbors at the free boundaries.