The generation mechanism of RX-mode waves in the equatorial plasmasphere has not been well understood. The Akebono passing through the storm time geomagnetic equator shows the possibility of the local enhancement of RX-mode waves in association with intense Z-mode waves in the equatorial region. We use the initial parameters inferred from observational data from around the plasma-wave generation region obtained by the Akebono satellite. A comparison of linear growth-rate calculations and simulation results is presented. The results of the simulation show two strong peaks related to the Z-mode and RX-mode waves, while the separation of these wave frequencies is equal to one cyclotron frequency. It is shown that electromagnetic Z- and RX-mode waves could be coupled by a nonlinear interaction.