Abstract: Under the condition of semi-geostrophical approximation and by means of the phase function method, the non-linear ordinary differential equation with latitudinal shearing flow is obtained. Then the conditions for the existence of limited amplitude periodical and isolated wave solutions are directly obtained on the basis of the qualitative theory of ordinary differential equations. It is proved that latitudinal shearing flow affects not only the existence but also the formation of waves, which indicates the non-linear features of waves and the influence of basic flows on undulations.