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Note on the modified nonlinear Schrödinger equation for deep water waves. (English) Zbl 0565.76020

It is shown that Zakharov’s integral equation [V. E. Zakharov, Zh. Prikl. Mekh. Tekh. Fiz. 9, 86-94 (1968)] yields the modified Schrödinger equation for the particular case of a narrow spectrum.

MSC:

76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
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References:

[1] Crawford, D. R.; Saffman, P. G.; Yuen, H. C., Evolution of a random inhomogeneous field of nonlinear deep water gravity waves, Wave Motion, 2, 1-16 (1980) · Zbl 0434.76018
[2] Crawford, D. R.; Lake, B. M.; Saffman, P. G.; Yuen, H. C., Stability of weakly nonlinear deep-water waves in two and three dimensions, J. Fluid Mech., 105, 177-191 (1981) · Zbl 0459.76011
[3] Dysthe, K. B., Note on a modification of the nonlinear Schrödinger equation for application to deep water waves, (Proc. Roy. Soc., A369 (1979)), 105-114 · Zbl 0429.76014
[4] Jones, D. S., Generalized Functions (1966), McGraw-Hill · Zbl 0149.09403
[5] Yuen, H. C.; Lake, B. M., Nonlinear dynamics of deep-water gravity waves, Advances in Applied Mechanics, 22, 67-229 (1982) · Zbl 0567.76026
[6] J. Appl. Mech. Tech. Phys., 9, 190-194 (1968), Translated in
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