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For nonlinear Schr\"odinger equations in less than or equal to fourdimension, with non-vanishing initial data at infinity, a new approach toderive the conservation law is obtained. Since this approach does not containapproximating procedure, the argument is simplified and some of technicalassumption of the nonlinearity to derive the conservation law and time globalsolutions, is removed.

The derivation of the conservation law for defocusing nonlinear Schroedinger equations with non-vanishing initial data at infinity