Symmetry results for decay solutions of elliptic systems in the whole space

In this paper, by using the Alexandrov-Serrin method of moving planes combined with maximum principles, we prove that the decaying positive solutions of a semi-linear elliptic system in the whole space are radially symmetric about some point. The system under our consideration includes the important physical interesting case, the stationary Schrödinger system for Bose-Einstein condensate.