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