  Lie symmetry analysis is applied to study the nonlinear rotating shallow
water equations. The 9-dimensional Lie algebra of point symmetries admitted by
the model is found. It is shown that the rotating shallow water equations are
related with the classical shallow water model with the change of variables.
The derived symmetries are used to generate new exact solutions of the rotating
shallow equations. In particular, a new class of time-periodic solutions with
quasi-closed particle trajectories is constructed and studied. The symmetry
reduction method is also used to obtain some invariant solutions of the model.
Examples of these solutions are presented with a brief physical interpretation.
