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Exact solutions describing Rossby waves and vortices in ocean propagatingalong the zonal direction at a constant velocity are considered for the(3+1)-dimensional nonlinear Charney-Obukhov equation. In the first part of ourwork, we give examples of solutions of the Charney-Obukhov equation thatsatisfy the nonlinear boundary conditions of the ocean, for a special case thatcorresponds to the "separation" of variables.

Solutions of the (3 + 1) dimensional Charney-Obukhov equation for the ocean, Part I: case of "separation'' of variables