Abstract: In this paper the nonlinear waves that are produced by geostrophic deviation in the barotropic atmosphere with the semi-geostrophic approximation (or geostrophic momentum approximation) are discussed. The analytical solution of this barotropic model is obtained. It is shown that the condition which brought elliptical function into existence is and the condition which brought solitary into existence is a=± If we defined M=a/ ,the above conditions changed into and M=±1.