Abstract
The ordinary nonlinear Schrödinger equation for deep water waves, found by perturbation analysis to
O
(∊
3
) in the wave-steepness ∊ ═
ka
, is shown to compare rather unfavourably with the exact calculations of Longuet-Higgins (1978
b
) for ∊ > 0.15, say. We show that a significant improvement can be achieved by taking the perturbation analysis one step further
O
(∊
4
). The dominant new effect introduced to order ∊
4
is the mean flow response to non-uniformities in the radiation stress caused by modulation of a finite amplitude wave.
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