Note on a modification to the nonlinear Schrödinger equation for application to deep water waves
1979 ◽
Vol 369
(1736)
◽
pp. 105-114
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Keyword(s):
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.
2013 ◽
Vol 43
(2)
◽
2000 ◽
Vol 29
(3-5)
◽
pp. 509-524
◽
2018 ◽
Vol 48
(1)
◽
pp. 59-68
◽
1977 ◽
Vol 83
(1)
◽
pp. 49-74
◽