O'Neil and Al'tshul et al.([1,2]) discussed the nonlinear theory of large-amplitude electron plasma waves (EPW). Franklin([3]) reported the experimental results of periodic amplitude variation of EPW caused by wave-particle interaction. In 1990([4]), we discussed the nonlinear Landau damping caused by electrons trapped in ion acoustic wave (IAW) with IAW drift instability. In the present note we will study theoretically and experimentally the three stages for the IAW amplitudes to develop from linear Landau damping (growing) to nonlinear effects. The experiments were performed in a double plasma device, which has been described previously([4]). At the pressure P approximate to 2.67 x 10(-2) Pa, the typical argon plasma parameters are: the plasma density N-e approximate to 5 x 10(8) cm(-3), the electron and ion temperature T-e approximate to 1 eV and T-e/T-i approximate to 15, thus the electron and ion thermal velocity V-e approximate to 4.2 x 10(7) cm . s(-1), V-i approximate to 4 x 10(4) cm . s(-1) respectively, and the electron-ion and nature particle collision frequency V-e approximate to 1 x 10(5) s(-1). The space potential difference between the two chambers (A and B) is modified very small (about Delta V-AB approximate to 0.1-0.5 V). This technique produces a slow electron drift V-d, which is in agreement with the theoretical prediction, e Delta V-AB = 1/2m V2/d < 1/3 T-e([4]). Usually it is obtained as Vd approximate to 1.4 x 10(7) cm . s(-1).