STUDY OF NONLINEAR ROSSBY WAVES IN THE ATMOSPHERE UNDER SEMI-GEOSTROPHIC APPROXIMATION^*

Under semi-geostrophic approximation the nonlinear ordinary differential equations are obtained for the motion in the barotropic and baroclinic atmospheres with the effects of zonal shear basic flow and topographic forcing included.Two constraints are acquired of finite-amplitude periodic and solitary waves in the original model with the aid of the phase-plane geometric qualitative theory of a dynamic system defined by the differential equation.The explicit solution of the nonlinear waves is found by means of the approximation method and some significant results are achieved.