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The paper is devoted to the group analysis of equations of motion oftwo-dimensional uniformly stratified rotating fluids used as a basic model ingeophysical fluid dynamics. It is shown that the nonlinear equations inquestion have a remarkable property to be self-adjoint.  This property is crucial for constructing conservation laws provided in thepresent paper. Invariant solutions are constructed using certain symmetries.The invariant solutions are used for defining internal wave beams.

Group Analysis of Nonlinear Internal Waves in Oceans. I: Self-adjointness, conservation laws, invariant solutions