Capillary waves in an inhomogeneous three-layer liquid with a free surface

In the domain of capillary waves, a bicubic dispersion relation is derived and analyzed for surface and internal capillary–gravitational waves in a three-layer liquid with a free surface. It is shown that the ratio of the internal wave amplitudes to the surface wave amplitudes is fairly large if the trivial condition of a “homogeneous liquid” is discarded. The amplitude ratio between the internal waves themselves (generated at different interfaces) may be both greater and smaller than unity depending on the physical parameters of the system. Specifically, it strongly depends on the densities of the layers and their thicknesses.