与一个非局域对称有关的Kaup-Kupershmidt方程新的精确解

NEW EXACT SOLUTIONS OF THE KAUP KUPERSHMIDT EQUATION RELATED TO A NON LOCAL SYMMETRY

利用ＫａｕｐＫｕｐｅｒｓｈｍｉｄｔ（ＫＫ）方程的一个非局域对称，可在两种不同的方法上找到方程新的精确解．首先，用标准的展开近似得到ＫＫ方程有限的ＬｉｅＢａ¨ｃｋｌｕｎｄ变换和单孤子解．其次，把一些局域对称与这个非局域对称组合起来，给出其群不变解。

Abstract Using a non local symmetry of the Kaup Kupershmidt (KK) equation, we find a new exact solution in two different ways. Firstly, using the standard prolongation approach, we obtain the finite Lie Ba¨cklund transformation and the single soliton solution of the KK equation. Secondly,combining some local symmetries and the nonlocal symmetry, we get the group invariant solution and obtain the new soliton solution of the KK equation.