In the recent 30 years,the investigation on the solitary and cnoidal wave of the nonlinear motion has attracted great interests in the atmosphere and ocean sciences.However,the most of former researches mainly emphasized on the aspects of the solving of solutions and the dynamic analyses of the wave,and rarely considered the relations between the diversified solitaries and the factual synoptic systems.The plateau vortex is one type of subsynoptic scale low-pressure vortex and a primary kind of synoptic systems over the Tibetan Plateau.It is the main rainfall system of the Tibetan Plateau in summer.Individual Plateau vortex can develop and move eastward out of the Tibetan Plateau coupled with the advantageous circulation pattern,which always gives rise to large-scale rainstorm or thunderstorm on the east side of the Tibetan Plateau(especially in Sichuan basin).Therefore,the study on Plateau vortex is not only an important problem of theoretical research on meteorology of the Tibetan Plateau,but also has practical meanings of improving the weather forecast accuracy in the area of the Tibetan Plateau and its east side.The KdV equation is derived from nonlinear inertial gravitational wave equation using the method of phase plane analysis and two types of solitary wave solutions with weather meanings are obtained by a direct integration method.We specially analyze the characteristics of singular solitary wave which has the association with the vortex over the Tibetan Plateau,and then discuss the effects of the plateau diabatic heating and the atmospheric stability on the origin,the movement,the vertical motion,the horizontal divergence,and the structure of warm core of the plateau vortex.It is proved in theory that the plateau vortex has the features of vortex eye and warm core similar to the tropical cyclone-like vortices(TCLV).