In 2019, Rostami and Zeitlin  reported a discovery of steady, long-living, slowly eastward-moving large-scale coherent twin cyclones, so-called “equatorial modon,” by means of a moist-convective rotating shallow water model.  Crudest barotropic features of MJO such as eastward propagation along the equator, slow phase speed, hydro-dynamical coherent structure, the convergent zone of moist-convection, are captured by Rostami and Zeitlin's modon. Having an exact solution of streamlines for internal and external regions of equatorial asymptotic modon is another feature of this structure. It is shown that such eastward-moving coherent dipolar structures can be produced during geostrophic adjustment of localized large-scale pressure anomalies in the diabatic moist-convective environment on the equator.