The linear dispersion relation – unaffected by wave amplitude – is for nonlinear waves also correct at the second order of the perturbation theory expansion, with the orders in terms of the wave steepness  (where a is wave amplitude). To the third order, and for deep water, the dispersion relation is
:  so  
This implies that large waves travel faster than small ones of the same frequency. This is only noticeable when the wave steepness  is large.