中文摘要：

二维( 2D )非线性的 Rossby 波浪由 Petviashviliequation 描述了，它是被调用了一 barotropic quasi-geostrophicpotential 涡度方程的因地球自转而引起的延期，能通过 thePetviashvili 的准确周期波浪的解决方案被调查方程，当时准确 anaiyticaJ Petviashviliequation 的周期波浪的答案被使用 Jacobi 获得椭圆形的函数扩大方法。它被看 thatperiodic 波浪 2D Rossby 答案能被这个方法获得，并且在限制案例中， 2DRossby soliton 答案也被获得。

英文摘要：

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.