A general description of wave motion supported and confined by the change in sign of the Coriolis parameter at the equator. A decomposition of the linearized equations of motion in vertical modes centered on the equator leads to a meridional structure that is a product of a Gaussian function and Hermite polynomials, with plane waves in the zonal direction. These solutions include trapped gravity waves, Rossby waves, and mixed Rossby–gravity waves, and together with Kelvin waves form a complete set.