Abstract: By using the equations of atmospheric dynamics with polar symmetry, the linear and nonlinear CISK heating processes are investigated. Using traveling wave method and theory of qualitative analysis of ordinary differential equation, the stability of the linear and nonlinear inertial-gravitational waves with CISK process and the influence of CISK process on the intensity and width of soliton inertial-gravitational waves are discussed. The results show that linear CISK process affects not only the intensity of soliton, but also the width of the soliton, nonlinear CISK process only affects intensity of the soliton.