This paper describes the third-order solution for the nonlinear internal and surface progressive water wave in a two-layer fluid. We use the perturbation method to develop a mathematical derivation. In the previous studies, the second- and third-order solutions derived by Umeyama (2002) and Song (2004) can not satisfy the boundary conditions. The present third-order asymptotic solution which satisfies the governing equation and boundary conditions is obtained. The numerical results demonstrate the influence of the ratio density and thickness of the two fluids on the interfacial and surface profiles as well as the wave frequency. The wave elevations at the free surface and the interface are calculated in different wave conditions under the thicknesses and densities ratio between the upper and lower layers in two-layer fluids. This simple theoretical solution can be used to analyze the different dynamic mechanisms between a interfacial wave induced by the given surface wave (IWSW) and a surface wave induced by the given interfacial wave (SWIW). The effect of on the wave height of SWIW is shown in Fig1. The height of SWIW is directly proportional to . However, the effect of on the wave height of IWSW is opposite. The height of SWIW and are in inverse proportion relation (see Fig. 2).
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