Abstract: The KdV equation is derived from nonlinear internal inertial gravitational wave equation using phase plane analysis method and two types of solitary wave solutions with weather meaings are obtained by a direct integration method.The characristics of singular solitary wave are specially discussed and the relationship between the vortex over the Tibetan plateau and this solitary wave is established,and the effects of plateau heating and atmospheric stability on the plateau vortex are analyzed.Morever,the features of vortex eye and warm core associated with the plateau vortex similar to tropical cyclone-like vortices (TCLV) are proved in theory.