Two-Dimensional Rossby Waves： Exact Solutions to Petviashvili Equation

The two-dimensional （2D） nonlinear Rossby waves described by the Petviashvili equation, which has been invoked as an ageostrophic extension of the barotropic quasi-geostrophic potential vorticity equation, can be investigated through the exact periodic-wave solutions for the Petviashvili equation, while the exact analytical periodic-wave solutions to the Petviashvili equation are obtained by using the Jacobi elliptic function expansion method. It is shown that periodicwave 2D Rossby solutions can be obtained by this method, and in the limit cases, the 213 Rossby soliton solutions are also obtained.

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