A. Gill, Some simple solutions for heat induced tropical circulation, Q. J. Roy. Met. Soc, vol.106, p.462, 1980.

W. A. Heckley and A. Gill, Some simple analytical solutions to the problem of forced equatorial long 186 waves, Q. J. Roy. Met. Soc, vol.110, pp.203-217, 1984.

R. N. Ferreira, W. H. Schubert, and J. J. Hack, Dynamical aspects of twin tropical cyclones asso-188 ciated with the madden-julian oscillation, J. Atmos. Sci, vol.53, pp.929-945, 1996.

A. Gill, Atmosphere -Ocean Dynamics, 1982.

T. Matsuno, Quasi-geostrophic motions in the equatorial area, J. Met. Soc. Japan, vol.44, pp.25-43, 1966.

G. N. Vallis, Atmospheric and Oceanic Fluid Dynamics, p.192, 2017.

V. Zeitlin, Geophysical Fluid Dynamics: Understanding (almost) everything with rotating shallow 193 water models, 2018.

J. Lesommer, G. M. Reznik, and V. Zeitlin, Nonlinear geostrophic adjustment of long-wave distur-195 bances in the shallow-water model on the equatorial beta-plane, J. Fluid Mech, vol.515, pp.135-170, 2004.

Y. Matsuda and H. Takayama, Evolution of disturbances and geostrophic adjustment on the sphere, 197 J. Met. Soc. Japan, vol.67, pp.949-965, 1989.

F. Bouchut, J. Lambaerts, G. Lapeyre, and V. Zeitlin, Fronts and nonlinear waves in a simpli-199 fied shallow-water model of the atmosphere with moisture and convection, Phys. Fluids, vol.21, 2009.

M. Rostami and V. Zeitlin, Improved moist-convective rotating shallow water model and its applica-202 tion to instabilities of hurricane-like vortices, Q. J. Roy. Met. Soc, vol.144, pp.1450-1462, 2018.

M. Rostami and V. Zeitlin, Influence of condensation and latent heat release upon barotropic and 204 baroclinic instabilities of atmospheric vortices in a rotating shallow water model on the f-plane, p.205

, Geoph. Astrophys. Fluid Dyn, vol.111, pp.1-31, 2017.

F. Bouchut, Chapter 4: Efficient numerical finite volume schemes for shallow water models, p.207

, Nonlinear Dynamics of Rotating Shallow Water: Methods and Advances, Edited Series on Advances 208 in Nonlinear Science and Complexity, vol.2, pp.189-256, 2007.

M. Rostami and V. Zeitlin, Eastward-moving convection-enhanced modons in shallow water in the 210 equatorial tangent plane, Phys. Fluids, vol.31, p.21701, 2019.

J. Yano and J. J. Tribbia, Tropical atmospheric Madden-Julian oscillation: a strongly nonlinear free 212 solitary Rossby wave?, J. Atmos. Sci, vol.74, pp.3473-3489, 2017.