Abstract
The two-dimensional (2D) nonlinear Rossby waves describedby the Petviashvili equation, which has been invoked as anageostrophic extension of the barotropic quasi-geostrophicpotential vorticity equation, can be investigated through theexact periodic-wave solutions for the Petviashvili equation,while the exact analytical periodic-wave solutions to thePetviashvili equation are obtained by using the Jacobielliptic function expansion method. It is shown that periodic-wave2D Rossby solutions can be obtained by this method, and in the limitcases, the 2D Rossby soliton solutions are also obtained.
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