The variation equation describing distance dependence of the beam waist of a fundamental Gaussian beam with high intensity propagating in logarithmically saturable nonlinear media has been deduced. The equation is formally consistent with that of a particle moving in potential well, so we can use the behavior of a particle moving in potential well to describe the breath mode of Gaussian beams. Having adopted the quadratic approximation of potential, we can solve the equation and get the approximately analytical solutions of Gaussiantyped breath mode. We analyze the incident condition dependence of its breath period and breath depth, and the conditions of Gaussian spatial solitons forming．