Abstract: By using symmetric equations of atmospheric dynamics in y-z plane with vertical and horizontal shear of wind,the nonlinear ordinary differential equation is derived with the method of travelling wave,its stability is discussed by the theory of nonlinear stability and KDV equation is solved.The infuences of the linear CISK,the nonlinear CISK,the Inertial-stability and vertical shear of wind on amplitude and width of the isolated inertial gravitational waves are discussed. We aim to understand deeply the formation and development of meso-scale synoptic systems (for example,squall,MCC and cold surge of Asia high) when we understand the factors of development of inertial-gravitational waves.