The analysis of observations shows that there exists a strong variability of stationary planetary wave (SPW) amplitudes during winter-time in the Northern hemisphere. Using a numerical model of the general circulation, the nonlinear response to an increase of the SPW amplitudes at the lower boundary is investigated. The results obtained show that nonlinear wave-wave and wave-mean flow interactions lead to the saturation of the SPW1 (planetary wave with zonal wave number one). Further increase of the SPW1 forcing at the lower boundary cased a substantial change of the mean flow in the lower stratosphere that limit the vertical penetration of the forced wave into the stratosphere. In result the SPW1 amplitude in the upper stratosphere and mesosphere becomes even smaller in comparison with case of a weak forcing. The analysis of the SPW2 sensitivity in the stratosphere to an increase of the lower boundary forcing shows that in this case the response is approximately linear at least for the realistic (observed) SPW2 amplitudes. A possible application of the results obtained to the problems of the sudden stratospheric warmings, stratospheric vacillations, and spring-time transition is shortly discussed.