K(m,n)方程的对称性约化

SYMMETRY REDUCTIONS OF THE K(m,n) EQUATION 

利用对称性约化的直接法,给出了具有非线性色散情况下的K(m,n)模型的所有对称性约化.从第一种约化方程的Painlev啨性质分析可知,K(m,n)模型仅当m=n+1和m=n+2时是可积的.特殊情况下(行波约化),这种约化的解可用一个积分表示.给出了K(m,1)和K(m,m)的一般孤波解的明显表达式.

By using a direct method of symmetry reductions, all the symmetry reductions of the K(m,n) equation with nonlinear dispersion are given. From the Painlevé analysis of the first type of the reduction equation, we know that K(m,n) model is Painlevé intgrable only if m=n+1 and m=n+2 . In a special case (the travelling wave reduction), the general reduction solution can be expressed by an integration. The general solitary wave solutions of the K(m,1) and K(m,m) models are also given in this paper.