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The group properties of the shallow‐water equations with the complete Coriolis force are the subject of this study. In particular, we apply the Lie theory to classify the system of three nonlinear partial differential equations according to the admitted Lie point symmetries. For each case of the classification problem, the one‐dimensional optimal system is determined. The results are applied for the derivation of new similarity solutions.

Shallow‐water equations with complete Coriolis force: Group properties and similarity solutions