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A mechanism for dispersion to automatically arise from the dispersionlessWhitham Modulation equations (WMEs) is presented, relying on the use of amoving frame. The speed of this is chosen to be one of the characteristicswhich emerge from the linearisation of the Whitham system, and assuming theseare real (and thus the WMEs are hyperbolic) morphs the WMEs into the Korteweg -de Vries (KdV) equation in the boosted co-ordinate. Strikingly, thecoefficients of the KdV equation are universal, in the sense that they aredetermined by abstract properties of the original Lagrangian density. Twoillustrative examples of the theory are given to illustrate how the KdV may beconstructed in practice. The first being a revisitation of the derivation ofthe KdV equation from shallow water flows, to highlight how the theory of thispaper fits into the existing literature. The second is a complex Klein-Gordonsystem, providing a case where the KdV equation may only arise with a movingframe.

Dispersive Dynamics in the Characteristic Moving Frame