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We obtain the global well-posedness and the scattering theory of the solution for the modified Davey–Stewartson systemin the energy spacein this paper. Since the interaction Morawetz estimate fails and the nonlinearity is non-local, we employ the concentration-compactness argument introduced by Kenig and Merle (Invent Math. 2006;166:645–675) to establish the scattering result.

Energy scattering of a modified Davey–Stewartson system in three dimensions