Higher asymptotic approximations for nonlinear internal waves in fluids

Abstract

Nonlinear problems of wave-packet propagation along the interface between the two fluids of different densities with taking into account the surface tension are investigated. Two problems are considered, the one for two half-spaces, the another for the layer over a half-space. Asymptotic solutions are developed on the basis of the method of multiple scale expansions. Unlike previous investigations dealing with only three approximations in this paper four asymptotic approximations have been developed by using symbolic algebra. The evolution equations are obtained in the form of the nonlinear higher-order Schrodinger equations. The stability of solutions is investigated. As a result, the new region of stability for capillary waves and the new region of instability for gravity waves have been discovered in the case of the layer of finite thickness unlike the case of two fluid half-spaces.