Abstract: By means of sn-function expansion method and cn-function expansion method, several kinds of explicit solutions to the coupled KdV equations with variable coefficients are obtained, which include three sets of periodic wave-like solutions. These solutions degenerate to solitary wave-like solutions at a certain limit. Some new solutions are presented.

Key words: cn-function method, sn-function method, periodic wave-like solution, solitary wave-like solution, coupled KdV equations with variable coefficient