  A mechanism for dispersion to automatically arise from the dispersionless
Whitham Modulation equations (WMEs) is presented, relying on the use of a
moving frame. The speed of this is chosen to be one of the characteristics
which emerge from the linearisation of the Whitham system, and assuming these
are real (and thus the WMEs are hyperbolic) morphs the WMEs into the Korteweg -
de Vries (KdV) equation in the boosted co-ordinate. Strikingly, the
coefficients of the KdV equation are universal, in the sense that they are
determined by abstract properties of the original Lagrangian density. Two
illustrative examples of the theory are given to illustrate how the KdV may be
constructed in practice. The first being a revisitation of the derivation of
the KdV equation from shallow water flows, to highlight how the theory of this
paper fits into the existing literature. The second is a complex Klein-Gordon
system, providing a case where the KdV equation may only arise with a moving
frame.
