关键词: KdV-mKdV equation, symmetry reduction, direct method, classical Lie approach ,

Abstract:  In this paper,some similarity reductions of the combined KdV-mKdV equation are given by using both the direct method introduced by Clarkson and Kruskal and the classical Lie aproach by Lakshmanan and Kaliappan.The similarity solutions obtained by the classical Lie approach is only the special case of that obtained by the direct method.

Key words: KdV-mKdV equation, symmetry reduction, direct method, classical Lie approach ,