Abstract
In this paper, we simplify the proof of M. Hamano in [13], scattering theory of the solution to (NLS system), by using the method from B. Dodson and J. Murphy in [10]. Firstly, we establish a criterion to ensure the solution scatters in H1(R5)×H1(R5). In order to verify the correctness of the condition in scattering criterion, we must exclude the concentration of mass near the origin. The interaction Morawetz estimate and Galilean transform characterize a decay estimate, which implies that the mass of the system cannot be concentrated.
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