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The effective dynamics of interacting waves for coupled Schrödinger-Korteweg-de Vries equations over a slowly varying random bottom is rigorously studied. One motivation for studying such a system is better understanding the unidirectional motion of interacting surface and internal waves for a fluid system that is formed of two immiscible layers. It was shown recently by Craig-Guyenne-Sulem  that in the regime where the internal wave has a large amplitude and a long wavelength, the dynamicsdoi:10.1051/mmnp/20127201 fatcat:7aj244ougjbxvnldmx4d3tsyou