The fourth-order nonlinear Schrödinger equation for the envelope of Stokes waves on the surface of a finite-depth fluid View Full Text


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Article Info

DATE

2003-07

AUTHORS

Yu. V. Sedletsky

ABSTRACT

The method of multiple scales is used to derive the fourth-order nonlinear Schrödinger equation (NSEIV) that describes the amplitude modulations of the fundamental harmonic of Stokes waves on the surface of a medium-and large-depth (compared to the wavelength) fluid layer. The new terms of this equation describe the third-order linear dispersion effect and the nonlinearity dispersion effects. As the nonlinearity and the dispersion decrease, the equation uniformly transforms into the nonlinear Schrödinger equation for Stokes waves on the surface of a finite-depth fluid that was first derived by Hasimoto and Ono. The coefficients of the derived equation are given in an explicit form as functions of kh (h is the fluid depth, and k is the wave number). As kh tends to infinity, these coefficients transform into the coefficients of the NSEIV that was first derived by Dysthe for an infinite depth. More... »

PAGES

180-193

Identifiers

URI

http://scigraph.springernature.com/pub.10.1134/1.1600810

DOI

http://dx.doi.org/10.1134/1.1600810

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1022475945


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