Abstract: This paper considers the problem of nonlinear stability of a liquid layer flowing down an inclined plane. A perturbation method, which proposed in the application of weakly nonlinear theory to the problem of stability of plane Poiseuille flow by H. Zhou, is now used here in subcritical range. The simplified boundary conditions are given in this paper.The situations for different Reynolds numbers and wave numbers are calculated. The results indicate that when the Renolds number is near the neutral curve, the...