中文摘要：

以小振幅波理论为基础,利用摄动方法研究了有背景流场存在时三层密度分层流体的毛细重力波,给出了三层成层状态下各层流体速度势的二阶渐近解及毛细重力波面位移的二阶Stokes波解.结果表明：一阶解及二阶解除了依赖于各层流体的厚度及密度,也依赖于表面张力和各层流体的背景流场.

英文摘要：

In this paper, Gravity-Capillary Water Waves in three-layer stratified fluid with background current axe investigated by using a perturbation method, and the second-order asymptotic solutions of the velocity potentials and the second-order Stokes solutions of the associated elevations of the Gravity-Capillaxy Water Waves are presented based on the small amplitude wave theory. As expected, both the first-order and second-order solutions derived depend on not only the depths and densities of the three-layer fluid but also the surface tension and the background current of the fluid.