Stiassnie, Michael Note on the modified nonlinear Schrödinger equation for deep water waves. (English) Zbl 0565.76020 Wave Motion 6, 431-433 (1984). 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. Cited in 32 Documents MSC: 76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction Keywords:Taylor expansion; integral equation; modified Schrödinger equation; narrow spectrum PDFBibTeX XMLCite \textit{M. Stiassnie}, Wave Motion 6, 431--433 (1984; Zbl 0565.76020) Full Text: DOI 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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.