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We consider the nonlinear model of an infinite oscillator chain embedded in a background field. We start from an appropriate modulation ansatz of the space-time periodic solutions to the linearized (microscopic) model and derive formally the associated (macroscopic) modulation equation, which turns out to be the nonlinear Schrödinger equation. Then we justify this necessary condition rigorously for the case of nonlinearities with cubic leading terms; i.e. we show that solutions that have thedoi:10.1088/0951-7715/17/2/011 fatcat:jpkh6lqfqzfytm353w44wdao74