组合KDV方程的新的相似约化

NEW SIMILARITY REDUCTIONS FOR THECOMBINED KDV EQUATION

利用Ｃｌａｒｋｓｏｎ和Ｋｒｕｓｋａｌ等建立的直接方法，得到了组合ＫＤＶ方程的新的相似约化，并表明相似解所满足的常微分方程具有Ｐａｉｎｌｅｖｅ’性质．

Using the direct method introduced by Clarkson and Kruskal,we obtain thenew similarity reductions of the combined KdV equation.We also show that the ordinary dif ferential equation which is satisfied by the similarity solution possess the Painleve' property.