Abstract: In this paper, the F-expansion method proposed recently is improved and applied to derive the cnoidal-like solutions of the general KdV and mKdV equations with variable coefficients. In the limit case, the soliton-like solutions with variable propagating speed and amplitude are obtained.

Key words: F-expansion method, Cnoidal-like solution, Soliton-like solution, KdV equation with variable coefficients, mKdV equation with variable coefficients