Application of Jacobi elliptic functions in the atmospheric and oceanic dynamics: studies on two-dimensional nonlinear Rossby waves
雅可比椭圆函数在大气和海洋动力学中的应用:二维非线性Rossby波研究

The two-dimensional(2-D) 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 studied by the exact periodic-wave solutions for the Petviashvili equation.The exact analytical periodic-wave solutions to the Petviashvili equation are obtained by using our extended generalization of Jacobi elliptic function expansion method.It is shown that more periodic-wave 2-D Rossby solutions can be obtained by this method.In the limit case,the 2-D Rossby soliton solutions can also be obtained.