Often for simulations of hypersonic boundary layer transition, disturbances are purposely added to the domain to either model flight-test or noisy wind tunnel freestream fluctuations, or simply to decrease the immense turnaround time necessary for numerical error to cause laminar-turbulent transition. However, these amplitudes are usually of small amplitude -- suitable to wall-resolved simulations -- rendering wall-modelled large eddy simulation (WMLES) incapable of sustaining the same disturbances before they are dissipated, without an ad-hoc increase and tuning of the disturbance amplitude. We present a solution to this issue by taking inspiration from the Korteweg–De Vries (KdV) equation. This non-linear, dispersive partial differential equation includes a third derivative term. In similar fashion, we add the third derivative of the momentum vector and total energy to the right-hand-side of the compressible Navier-Stokes equations as a subgrid-scale (SGS) transition model to model the dispersion and interaction of instability waves necessary for breakdown to turbulence. In doing so, we allow for the use of the same disturbance amplitudes as in a direct numerical simulation (DNS) but with a grid suitable for a WMLES.