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74J30The maximal group of Lie point symmetries of a system of nonlinearequations used in geophysical fluid dynamics is presented.  The Lie algebra of this group is infinite-dimensional and involves threearbitrary functions of time. The invariant solution under the rotation anddilation is constructed. Qualitative analysis of the invariant solution isprovided and the energy of this solution is presented.

Group Analysis of Nonlinear Internal Waves in Oceans. II: The symmetries and rotationally invariant solution