On periodic inertia-gravity waves of finite amplitude propagating without change of form at sharp density-gradient interfaces in the rotating fluid

Existence of finite-amplitude inertia-gravity waves propagating without change of form is proved in the two-layer rotating shallow water model. We find exact solutions of the full equations of motion corresponding to such waves. The form of the nonlinear waves depends on the parameters of the model (density and height ratios of the layers) and on the phase speed. Three distinct families of waves having different forms and responding differently to the increase of amplitude are identified.