Standing equatorial wave modes are shown to be exact solutions of the forced, linear, inviscid shallow water equations when the forcing is zonally uniform and at a single frequency. If the forcing is equatorially confined in the meridional direction, then so is the directly forced response and the standing mode does not lealr. energy away from the equator....
Gent, Peter R.. 1981. "Forced standing equatorial ocean wave modes." Journal of Marine Research 39, (4). https://elischolar.library.yale.edu/journal_of_marine_research/1565